Spatially multiplexed volume Bragg gratings with varied refractive index modulations for waveguide display

ABSTRACT

A waveguide display includes a waveguide transparent to visible light, a first volume Bragg grating (VBG) on the waveguide and characterized by a first refractive index modulation, and a second reflection VBG on the waveguide and including a plurality of regions characterized by different respective refractive index modulations. The first reflection VBG is configured to diffract display light in a first wavelength range and a first field of view (FOV) range such that the display light in the first wavelength range and the first FOV range propagates in the waveguide through total internal reflection to the plurality of regions of the second reflection VBG. The plurality of regions of the second reflection VBG are configured to diffract the display light in different respective wavelength ranges within the first wavelength range and the first FOV range.

CROSS-REFERENCE TO RELATED APPLICATION

This patent application claims priority to U.S. Provisional PatentApplication Ser. No. 62/891,167, filed Aug. 23, 2019, entitled “VolumeBragg Grating-Based Waveguide Display,” the disclosure of which ishereby incorporated by reference in its entirety for all purposes.

BACKGROUND

An artificial reality system, such as a head-mounted display (HMD) orheads-up display (HUD) system, generally includes a near-eye display(e.g., in the form of a headset or a pair of glasses) configured topresent content to a user via an electronic or optic display within, forexample, about 10-20 mm in front of the user's eyes. The near-eyedisplay may display virtual objects or combine images of real objectswith virtual objects, as in virtual reality (VR), augmented reality(AR), or mixed reality (MR) applications. For example, in an AR system,a user may view both images of virtual objects (e.g., computer-generatedimages (CGIs)) and the surrounding environment by, for example, seeingthrough transparent display glasses or lenses (often referred to asoptical see-through).

One example of an optical see-through AR system may use awaveguide-based optical display, where light of projected images may becoupled into a waveguide (e.g., a transparent substrate), propagatewithin the waveguide, and be coupled out of the waveguide at differentlocations. In some implementations, the light of the projected imagesmay be coupled into or out of the waveguide using a diffractive opticalelement, such as a grating. Light from the surrounding environment maypass through a see-through region of the waveguide and reach the user'seyes as well.

SUMMARY

This disclosure relates generally to volume Bragg grating-basedwaveguide displays for near-eye display. More specifically, disclosedherein are techniques for expanding the eyebox, reducing display haze,reducing physical size, improving optical efficiency, reducing opticalartifacts, and increasing field of view of optical see-through near-eyedisplay systems using volume Bragg grating (VBG) couplers. Variousinventive embodiments are described herein, including devices, systems,methods, and the like.

According to some embodiments, a waveguide display may include asubstrate, a first reflection VBG on the substrate and characterized bya first refractive index modulation, and a second reflection VBG on thesubstrate and including a first region and a second region. The firstreflection VBG may be configured to diffract display light in a firstwavelength range such that the display light in the first wavelengthrange propagates in the substrate through total internal reflection tothe first region and the second region of the second reflection VBG. Thefirst region of the second reflection VBG may be characterized by asecond refractive index modulation lower than the first refractive indexmodulation and may be configured to diffract display light in a secondwavelength range that is within the first wavelength range. The secondregion of the second reflection VBG may be characterized by a thirdrefractive index modulation greater than the second refractive indexmodulation and may be configured to diffract display light in a thirdwavelength range that includes and is larger than the second wavelengthrange. The first region and the second region of the second reflectionVBG may be arranged such that the display light in the first wavelengthrange reaches the first region before reaching the second region.

In some embodiments, the first reflection VBG and the second reflectionVBG may have a same grating vector in a plane perpendicular to a surfacenormal direction of the substrate. The third refractive index modulationmay be equal to or less than the first refractive index modulation, andthe first wavelength range may be the same as or includes the thirdwavelength range. In some embodiments, the second reflection VBG mayfurther include a third region between the first region and the secondregion, where the third region may be characterized by a fourthrefractive index modulation greater than the second refractive indexmodulation but lower than the third refractive index modulation and maybe configured to diffract display light in a fourth wavelength rangethat includes the second wavelength range and is within the thirdwavelength range.

In some embodiments, the waveguide display may further include a thirdreflection VBG multiplexed with the first reflection VBG andcharacterized by a fourth refractive index modulation, and a fourthreflection VBG multiplexed with the second reflection VBG in the firstregion and second region. The third reflection VBG may be configured todiffract display light in a fourth wavelength range such that thedisplay light in the fourth wavelength range propagates in the substratethrough total internal reflection to the first region and the secondregion of the fourth reflection VBG. The first region of the fourthreflection VBG may be characterized by a fifth refractive indexmodulation lower than the fourth refractive index modulation and may beconfigured to diffract display light in a fifth wavelength range that iswithin the fourth wavelength range. The second region of the fourthreflection VBG may be characterized by a sixth refractive indexmodulation greater than the fifth refractive index modulation and may beconfigured to diffract display light in a sixth wavelength range thatincludes and is larger than the fifth wavelength range.

In some embodiments, the first reflection VBG may be configured todiffract display light in the first wavelength range and a first fieldof view (FOV) range, and diffract display light in a fourth wavelengthrange and a second FOV range different from the first FOV range. In someembodiments, the substrate may be transparent to visible light, and thesecond reflection VBG may be transparent to visible light from anambient environment. In some embodiments, the first reflection VBG maybe configured to couple the display light in the first wavelength rangeinto the substrate, and the second reflection VBG may be configured tocouple the display light in the first wavelength range out of thesubstrate. In some embodiments, the waveguide display may furtherinclude a third grating and a fourth grating, where the third gratingmay be configured to diffract the display light in the first wavelengthrange from the first reflection VBG to the fourth grating, and thefourth grating may be configured to diffract the display light in thefirst wavelength range at two or more regions of the fourth grating tothe second reflection VBG. The third grating and the fourth grating mayhave a same grating vector in a plane perpendicular to a surface normaldirection of the substrate.

In some embodiments, the waveguide display may include an input couplerconfigured to couple the display light in the first wavelength rangeinto the substrate, and an output coupler configured to couple thedisplay light diffracted by the second reflection VBG out of thesubstrate. The input coupler and the output coupler may includemultiplexed VBGs. In some embodiments, the waveguide display may includea light source configured to generate the display light, and projectoroptics configured to collimate the display light and direct the displaylight to the first reflection VBG.

According to certain embodiments, a waveguide display may include awaveguide transparent to visible light, a first VBG on the waveguide andcharacterized by a first refractive index modulation, and a secondreflection VBG on the waveguide and including a plurality of regionscharacterized by different respective refractive index modulations. Thefirst reflection VBG may be configured to diffract display light in afirst wavelength range and a first FOV range such that the display lightin the first wavelength range and the first FOV range may propagate inthe waveguide through total internal reflection to the plurality ofregions of the second reflection VBG. The plurality of regions of thesecond reflection VBG may be configured to diffract the display light indifferent respective wavelength ranges within the first wavelength rangeand the first FOV range. The first reflection VBG and the secondreflection VBG may have a same grating vector in a plane perpendicularto a surface normal direction of the waveguide.

In some embodiments of the waveguide display, the first refractive indexmodulation and at least one of the different respective refractive indexmodulations of the plurality of regions of the second reflection VBG maybe greater than a minimum refractive index modulation for diffractionefficiency saturation. In some embodiments, the plurality of regions ofthe second reflection VBG may be configured such that the display lightin the first wavelength range and the first FOV range may reach a firstregion of the plurality of regions having a second refractive indexmodulation before reaching a second region of the plurality of regionshaving a third refractive index modulation that is greater than thesecond refractive index modulation.

In some embodiments, the first reflection VBG may be configured tocouple the display light in the first wavelength range and the first FOVrange into the waveguide, and the second reflection VBG may beconfigured to couple the display light in the first wavelength range andthe first FOV range out of the waveguide and may be transparent tovisible light from an ambient environment. In some embodiments, thewaveguide display may also include a third grating and a fourth grating.The third grating may be configured to diffract the display light in thefirst wavelength range and the first FOV range from the first reflectiongrating to the fourth grating. The fourth grating may be configured todiffract the display light in the first wavelength range and the firstFOV range at two or more regions of the fourth grating to the secondreflection VBG. The third grating and the fourth grating may have a samegrating vector in a plane perpendicular to a surface normal direction ofthe waveguide.

This summary is neither intended to identify key or essential featuresof the claimed subject matter, nor is it intended to be used inisolation to determine the scope of the claimed subject matter. Thesubject matter should be understood by reference to appropriate portionsof the entire specification of this disclosure, any or all drawings, andeach claim. The foregoing, together with other features and examples,will be described in more detail below in the following specification,claims, and accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

Illustrative embodiments are described in detail below with reference tothe following figures.

FIG. 1 is a simplified block diagram of an example of an artificialreality system environment including a near-eye display system accordingto certain embodiments.

FIG. 2 is a perspective view of an example of a near-eye display systemin the form of a head-mounted display (HMD) device for implementing someof the examples disclosed herein.

FIG. 3 is a perspective view of an example of a near-eye display systemin the form of a pair of glasses for implementing some of the examplesdisclosed herein.

FIG. 4 is a simplified diagram illustrating an example of an opticalsystem in a near-eye display system.

FIG. 5 illustrates an example of an optical see-through augmentedreality system including a waveguide display for exit pupil expansionaccording to certain embodiments.

FIG. 6 illustrates an example of an optical see-through augmentedreality system including a waveguide display for exit pupil expansionaccording to certain embodiments.

FIG. 7A illustrates the spectral bandwidth of an example of a reflectionvolume Bragg grating (VBG) and the spectral bandwidth of an example of atransmissive surface-relief grating (SRG). FIG. 7B illustrates theangular bandwidth of an example of a reflection VBG and the angularbandwidth of an example of a transmissive SRG.

FIG. 8A illustrates an example of an optical see-through augmentedreality system including a waveguide display and surface-relief gratingsfor exit pupil expansion according to certain embodiments. FIG. 8Billustrates an example of an eye box including two-dimensionalreplicated exit pupils according to certain embodiments.

FIG. 9A illustrates wave vectors of light diffracted by examples ofsurface-relief gratings for exit pupil expansion in a waveguide displayand exit pupils for multiple colors.

FIG. 9B illustrates the field-of-view clipping by the examples ofsurface-relief gratings for exit pupil expansion in the waveguidedisplay.

FIG. 10A illustrates an example of a volume Bragg grating-basedwaveguide display according to certain embodiments. FIG. 10B illustratesa top view of the example of the volume Bragg grating-based waveguidedisplay shown in FIG. 10A. FIG. 10C illustrates a side view of theexample of the volume Bragg grating-based waveguide display shown inFIG. 10A.

FIG. 11 illustrates light dispersion in an example of a volume Bragggrating-based waveguide display according to certain embodiments.

FIG. 12A illustrates an example of a volume Bragg grating (VBG). FIG.12B illustrates the Bragg condition for the volume Bragg grating shownin FIG. 12A.

FIG. 13A illustrates a front view of an example of a volume Bragggrating-based waveguide display with exit pupil expansion and dispersionreduction according to certain embodiments. FIG. 13B illustrates a sideview of the example of the volume Bragg grating-based waveguide displayshown in FIG. 13A.

FIG. 14A illustrates the propagation of light from different fields ofview in a reflection volume Bragg grating-based waveguide displayaccording to certain embodiments. FIG. 14B illustrates the propagationof light from different fields of view in a transmission volume Bragggrating-based waveguide display according to certain embodiments.

FIG. 15 illustrates an example of a reflection volume Bragggrating-based waveguide display with exit pupil expansion and dispersionreduction according to certain embodiments.

FIG. 16 illustrates an example of a transmission volume Bragggrating-based waveguide display with exit pupil expansion andform-factor reduction according to certain embodiments.

FIG. 17A illustrates an example of a transmission volume Bragg gratingin a waveguide display according to certain embodiments. FIG. 17Billustrates an example of a transmission VBG in a waveguide displaywhere light diffracted by the reflection VBG is not totally reflectedand guided in the waveguide. FIG. 17C illustrates an example of areflection volume Bragg grating in a waveguide display according tocertain embodiments. FIG. 17D illustrates an example of a reflection VBGin a waveguide display where light diffracted by the transmission VBG isnot totally reflected and guided in the waveguide.

FIG. 18A illustrates the light dispersion by an example of a reflectionvolume Bragg grating in a waveguide display according to certainembodiments. FIG. 18B illustrates the light dispersion by an example ofa transmission volume Bragg grating in a waveguide display according tocertain embodiments.

FIG. 19A is a front view of an example of a volume Bragg grating-basedwaveguide display with exit pupil expansion and dispersion reductionaccording to certain embodiments.

FIG. 19B is a side view of the example of the volume Bragg grating-basedwaveguide display including an image projector and multiple polymerlayers according to certain embodiments.

FIG. 20A illustrates another example of a volume Bragg grating-basedwaveguide display with exit pupil expansion, dispersion reduction,form-factor reduction, and power efficiency improvement according tocertain embodiments. FIG. 20B illustrates examples of replicated exitpupils at an eyebox of the volume Bragg grating-based waveguide displayshown in FIG. 20A.

FIG. 21A illustrates an example of a volume Bragg grating-basedwaveguide display with exit pupil expansion, dispersion reduction, andform-factor reduction according to certain embodiments. FIG. 21Billustrates an example of a volume Bragg grating-based waveguide displaywith exit pupil expansion, dispersion reduction, form-factor reduction,and efficiency improvement according to certain embodiments.

FIG. 22A is a front view of an example of a volume Bragg grating-basedwaveguide display including two image projectors according to certainembodiments. FIG. 22B is a side view of the example of volume Bragggrating-based waveguide display including two image projectors accordingto certain embodiments.

FIG. 23A is a front view of an example of a volume Bragg grating-basedwaveguide display including a single image projector and gratings forfield-of-view stitching according to certain embodiments. FIG. 23B is aside view of the example of the volume Bragg grating-based waveguidedisplay with the single image projector and the gratings forfield-of-view stitching according to certain embodiments.

FIG. 24 illustrates an example of a volume Bragg grating-based waveguidedisplay including multiple grating layers for different fields of viewand/or light wavelengths according to certain embodiments.

FIG. 25 illustrates the fields of view of multiple gratings in anexample of a volume Bragg grating-based waveguide display according tocertain embodiments.

FIG. 26A illustrates the diffraction of light of different colors fromdifferent corresponding fields of view by an example of a volume Bragggrating. FIG. 26B illustrates the relationship between grating periodsof volume Bragg gratings and the corresponding fields of view forincident light of different colors.

FIG. 27A illustrates the diffraction efficiencies of examples oftransmission volume Bragg gratings with the same thickness but differentrefractive index modulations. FIG. 27B illustrates the diffractionefficiencies of examples of reflection volume Bragg gratings with thesame thickness but different refractive index modulations.

FIG. 28A illustrates the diffraction efficiency of an example of atransmission volume Bragg grating with a first refractive indexmodulation as a function of the deviation of the incident angle from theBragg condition. FIG. 28B illustrates the diffraction efficiency of anexample of a transmission volume Bragg grating with a second refractiveindex modulation as a function of the deviation of the incident anglefrom the Bragg condition. FIG. 28C illustrates the diffractionefficiency of an example of a transmission volume Bragg grating with athird refractive index modulation as a function of the deviation of theincident angle from the Bragg condition. FIG. 28D illustrates thediffraction efficiency of an example of a transmission volume Bragggrating with a fourth refractive index modulation as a function of thedeviation of the incident angle from the Bragg condition.

FIG. 29A illustrates the diffraction efficiency of an example of areflection volume Bragg grating with a first refractive index modulationas a function of the deviation of the incident angle from the Braggcondition. FIG. 29B illustrates the diffraction efficiency of an exampleof a reflection volume Bragg grating with a second refractive indexmodulation as a function of the deviation of the incident angle from theBragg condition. FIG. 29C illustrates the diffraction efficiency of anexample of a reflection volume Bragg grating with a third refractiveindex modulation as a function of the deviation of the incident anglefrom the Bragg condition. FIG. 29D illustrates the diffractionefficiency of an example of a reflection volume Bragg grating with afourth refractive index modulation as a function of the deviation of theincident angle from the Bragg condition.

FIG. 30A illustrates diffraction efficiencies of an example of atransmission VBG with a first refractive index modulation for blue lightfrom different fields of view. FIG. 30B illustrates diffractionefficiencies of the example of transmission VBG with the firstrefractive index modulation for green light from different fields ofview. FIG. 30C illustrates diffraction efficiencies of the example oftransmission VBG with the first refractive index modulation for redlight from different fields of view. FIG. 30D illustrates diffractionefficiencies of an example of a transmission VBG with a secondrefractive index modulation for blue light from different fields ofview. FIG. 30E illustrates diffraction efficiencies of the example oftransmission VBG with the second refractive index modulation for greenlight from different fields of view. FIG. 30F illustrates diffractionefficiencies of the example of transmission VBG with the secondrefractive index modulation for red light from different fields of view.FIG. 30G illustrates diffraction efficiencies of an example of atransmission VBG with a third refractive index modulation for blue lightfrom different fields of view. FIG. 30H illustrates diffractionefficiencies of the example of transmission VBG with the thirdrefractive index modulation for green light from different fields ofview. FIG. 30I illustrates diffraction efficiencies of the example oftransmission VBG with the third refractive index modulation for redlight from different fields of view.

FIG. 31A illustrates the minimum refractive index modulations oftransmission volume Bragg gratings with different grating periods inorder to achieve diffraction saturation for light of different colors.FIG. 31B shows the maximum refractive index modulations of transmissiongratings having different grating periods in order to avoid refractiveindex modulation saturation for blue, green, and red light. FIG. 31Cillustrates an example of a grating layer including multiplexed VBGs ofdifferent pitches and refractive index modulations for optimizeddiffraction efficiency and uniformity according to certain embodiments.

FIG. 32A illustrates FOV crosstalk caused by examples of multiplexedvolume Bragg gratings. FIG. 32B illustrates the relationship betweengrating periods of volume Bragg gratings and the corresponding fields ofview for incident light of different colors.

FIG. 33A illustrates linewidths of Bragg peaks of transmission volumeBragg gratings and reflection volume Bragg gratings for different fieldsof view. FIG. 33B illustrates examples of Bragg peaks of transmissionvolume Bragg gratings for different fields of view. FIG. 33C illustratesexamples of Bragg peaks of reflection volume Bragg gratings fordifferent fields of view.

FIG. 34A illustrates trade-off between crosstalk and efficiency in anexample of a multiplexed volume Bragg grating. FIG. 34B illustratestrade-off between crosstalk and efficiency in an example of amultiplexed volume Bragg grating.

FIG. 35A illustrates the relationship between the minimum diffractionefficiency and the total refractive index modulation and thecorresponding crosstalk in multiplexed transmission volume Bragggratings. FIG. 35B illustrates the relationship between the minimumdiffraction efficiency and the total refractive index modulation and thecorresponding crosstalk in multiplexed reflection volume Bragg gratings.

FIG. 36 illustrates an example of a waveguide display includingspatially multiplexed reflection volume Bragg gratings having differentrefractive index modulations according to certain embodiments.

FIG. 37 illustrates an example of a waveguide display including twomultiplexed volume Bragg gratings and a polarization convertor betweenthe two multiplexed volume Bragg gratings according to certainembodiments.

FIG. 38 illustrates an example of a waveguide display including ananti-reflection layer and an angular-selective transmissive layeraccording to certain embodiments.

FIG. 39 is a simplified block diagram of an example of an electronicsystem in an example of a near-eye display according to certainembodiments.

The figures depict embodiments of the present disclosure for purposes ofillustration only. One skilled in the art will readily recognize fromthe following description that alternative embodiments of the structuresand methods illustrated may be employed without departing from theprinciples, or benefits touted, of this disclosure.

In the appended figures, similar components and/or features may have thesame reference label. Further, various components of the same type maybe distinguished by following the reference label by a dash and a secondlabel that distinguishes among the similar components. If only the firstreference label is used in the specification, the description isapplicable to any one of the similar components having the same firstreference label irrespective of the second reference label.

DETAILED DESCRIPTION

This disclosure relates generally to volume Bragg grating (VBG)-basedwaveguide display for near-eye display systems. In a near-eye displaysystem, it is generally desirable to expand the eyebox, reduce displayhaze, improve image quality (e.g., resolution and contrast), reducephysical size, increase power efficiency, and increase the field ofview. In a waveguide-based near-eye display system, light of projectedimages may be coupled into a waveguide (e.g., a transparent substrate),propagate within the waveguide, and be coupled out of the waveguide atdifferent locations to replicate exit pupils and expand the eyebox. Twoor more gratings may be used to expand the exit pupil in two dimensions.In a waveguide-based near-eye display system for augmented realityapplications, light from the surrounding environment may pass through atleast a see-through region of the waveguide display (e.g., thetransparent substrate) and reach the user's eyes. In someimplementations, the light of the projected images may be coupled intoor out of the waveguide using diffractive optical elements, such asgratings.

Optical couplers implemented using diffractive optical elements may havea limited field of view due to the angular dependence of gratingefficiency. Therefore, light incident on the couplers from multipleincident angles (e.g., from different fields of view) may not bediffracted at equivalent or similar efficiency. In addition, couplersimplemented using diffractive optical elements may cause dispersionbetween light of different colors and may have different diffractionangles for light of different colors. Therefore, different colorcomponents in a color image may not overlap with each other. Thus, thequality of the displayed image (e.g., color reproduction neutrality) maybe reduced. Furthermore, the fields of view for light of differentcolors may be reduced or partially clipped due to the light dispersionand the limited range of wave vectors of light that can be guided by thewaveguide display. To reduce the dispersion and improve the field ofview (FOV) range and diffraction efficiency, thick transmission and/orreflection VBG gratings that include many multiplexed gratings to coverdifferent fields of view for different color components may be used,which may be impractical in many cases and/or may cause significantdisplay and see-through haze due to the thickness of the gratings andthe large number of exposures to record the multiplexed VBG gratings.For example, in some cases, transmission VBG gratings with a thicknessof greater than 1 mm may be needed in order to reduce the dispersion andachieve a desired FOV range and diffraction efficiency. Reflection VBGgratings with a relatively lower thickness may be used to achieve thedesired performance. However, with reflection gratings, the gratings fortwo-dimensional pupil expansion may not overlap and thus the physicalsize of the waveguide display may be large and the display haze maystill be significant.

According to certain embodiments, two VBG gratings (or two portions of asame grating) with matching grating vectors (e.g., having the samegrating vector in a plane perpendicular to a surface normal direction ofthe transparent substrate) may be used to diffract display light andexpand the exit pupil in one dimension. The two VBG gratings maycompensate for the dispersion of display light caused by each other toreduce the overall dispersion, due to the opposite Bragg conditions(e.g., +1 order and −1 order diffractions) at the two VBG gratings.Therefore, thin VBG gratings may be used and may still achieve thedesired resolution. Because of the dispersion compensation, thintransmission VBG gratings may be used to achieve the desired resolution,and the gratings for the two-dimensional pupil expansion may at leastpartially overlap to reduce the physical size of the waveguide display.

In some embodiments, to achieve the desired FOV, coupling efficiency,and coupling efficiency uniformity across the full FOV and colorspectrum, multiple VBG layers including multiplexed VBGs may be formedon one or more waveguide plates. Each VBG layer may be used to couplelight in a certain FOV and/or color range at a relatively highefficiency, and the combination of the multiple VBG layers may providefull coverage of the desired FOV and color range at relatively high anduniform coupling efficiencies.

In some embodiments, a first pair of VBG gratings (or two portions of agrating) may be used to expand the exit pupil in one dimension andcompensate for the dispersion caused by each other, and a second pair ofVBG gratings (or two portions of a grating) may be used to expand theexit pupil in another dimension and may compensate for the dispersioncaused by each other. Thus, the exit pupil may be replicated in twodimensions and the resolution of the displayed images may be high inboth dimensions.

According to certain embodiments, the first pair and/or the second pairof gratings may each include multiplexed reflection volume Bragggratings. The multiplexed reflection VBGs may include reflection VBGsthat may have high diffraction efficiencies and low crosstalk betweenreflection VBGs in the multiplexed reflection VBGs. In some embodiments,the reflection VBGs may have refractive index modulations greater thanthe minimum refractive index modulation for diffraction efficiencysaturation, and thus may have high diffraction efficiencies and widefull-width-half-magnitude (FWHM) wavelength ranges and/or FWHM angularranges. As such, fewer reflection VBGs may be used to cover thewavelength range of the light source and the full FOV to improve theefficiency and performance of the waveguide display.

In some embodiments, each of the first pair of gratings and/or thesecond pair of gratings may include a first reflection VBG characterizedby a first refractive index modulation, and a second reflection VBGincluding a plurality of regions characterized by different respectiverefractive index modulations. The first reflection VBG may be configuredto diffract display light in a first wavelength range (and/or a firstFOV range) such that the display light in the first wavelength range(and/or the first FOV range) may propagate in the waveguide throughtotal internal reflection to the plurality of regions of the secondreflection VBG. The plurality of regions of the second reflection VBGmay be configured to diffract the display light in different respectivewavelength (and/or FOV) ranges within the first wavelength range (and/orthe first FOV range) due to the different respective refractive indexmodulations. The first reflection VBG and the second reflection VBG mayhave a same grating vector in a plane perpendicular to a surface normaldirection of the waveguide to reduce dispersion. The first refractiveindex modulation and at least one of the different respective refractiveindex modulations of the plurality of regions of the second reflectionVBG may be greater than the minimum refractive index modulation fordiffraction efficiency saturation. The plurality of regions of thesecond reflection VBG may be arranged such that the display light in thefirst wavelength range (and/or the first FOV range) reaches a firstregion having a lower refractive index modulation in the plurality ofregions before reaching a second region having a higher refractive indexmodulation in the plurality of regions. In this way, display light in anarrower portion of the first wavelength range (and/or the first FOV)may be diffracted by the first region, and display light in the firstwavelength range (and/or the first FOV) but outside of the narrowerportion may be diffracted by the second region.

In the following description, various inventive embodiments aredescribed, including devices, systems, methods, and the like. For thepurposes of explanation, specific details are set forth in order toprovide a thorough understanding of examples of the disclosure. However,it will be apparent that various examples may be practiced without thesespecific details. For example, devices, systems, structures, assemblies,methods, and other components may be shown as components in blockdiagram form in order not to obscure the examples in unnecessary detail.In other instances, well-known devices, processes, systems, structures,and techniques may be shown without necessary detail in order to avoidobscuring the examples. The figures and description are not intended tobe restrictive. The terms and expressions that have been employed inthis disclosure are used as terms of description and not of limitation,and there is no intention in the use of such terms and expressions ofexcluding any equivalents of the features shown and described orportions thereof. The word “example” is used herein to mean “serving asan example, instance, or illustration.” Any embodiment or designdescribed herein as “example” is not necessarily to be construed aspreferred or advantageous over other embodiments or designs.

FIG. 1 is a simplified block diagram of an example of an artificialreality system environment 100 including a near-eye display 120 inaccordance with certain embodiments. Artificial reality systemenvironment 100 shown in FIG. 1 may include near-eye display 120, anoptional external imaging device 150, and an optional input/outputinterface 140, each of which may be coupled to an optional console 110.While FIG. 1 shows an example of artificial reality system environment100 including one near-eye display 120, one external imaging device 150,and one input/output interface 140, any number of these components maybe included in artificial reality system environment 100, or any of thecomponents may be omitted. For example, there may be multiple near-eyedisplays 120 monitored by one or more external imaging devices 150 incommunication with console 110. In some configurations, artificialreality system environment 100 may not include external imaging device150, optional input/output interface 140, and optional console 110. Inalternative configurations, different or additional components may beincluded in artificial reality system environment 100.

Near-eye display 120 may be a head-mounted display that presents contentto a user. Examples of content presented by near-eye display 120 includeone or more of images, videos, audio, or any combination thereof. Insome embodiments, audio may be presented via an external device (e.g.,speakers and/or headphones) that receives audio information fromnear-eye display 120, console 110, or both, and presents audio databased on the audio information. Near-eye display 120 may include one ormore rigid bodies, which may be rigidly or non-rigidly coupled to eachother. A rigid coupling between rigid bodies may cause the coupled rigidbodies to act as a single rigid entity. A non-rigid coupling betweenrigid bodies may allow the rigid bodies to move relative to each other.In various embodiments, near-eye display 120 may be implemented in anysuitable form-factor, including a pair of glasses. Some embodiments ofnear-eye display 120 are further described below with respect to FIGS. 2and 3. Additionally, in various embodiments, the functionality describedherein may be used in a headset that combines images of an environmentexternal to near-eye display 120 and artificial reality content (e.g.,computer-generated images). Therefore, near-eye display 120 may augmentimages of a physical, real-world environment external to near-eyedisplay 120 with generated content (e.g., images, video, sound, etc.) topresent an augmented reality to a user.

In various embodiments, near-eye display 120 may include one or more ofdisplay electronics 122, display optics 124, and an eye-tracking unit130. In some embodiments, near-eye display 120 may also include one ormore locators 126, one or more position sensors 128, and an inertialmeasurement unit (IMU) 132. Near-eye display 120 may omit any ofeye-tracking unit 130, locators 126, position sensors 128, and IMU 132,or include additional elements in various embodiments. Additionally, insome embodiments, near-eye display 120 may include elements combiningthe function of various elements described in conjunction with FIG. 1.

Display electronics 122 may display or facilitate the display of imagesto the user according to data received from, for example, console 110.In various embodiments, display electronics 122 may include one or moredisplay panels, such as a liquid crystal display (LCD), an organic lightemitting diode (OLED) display, an inorganic light emitting diode (ILED)display, a micro light emitting diode (μLED) display, an active-matrixOLED display (AMOLED), a transparent OLED display (TOLED), or some otherdisplay. For example, in one implementation of near-eye display 120,display electronics 122 may include a front TOLED panel, a rear displaypanel, and an optical component (e.g., an attenuator, polarizer, ordiffractive or spectral film) between the front and rear display panels.Display electronics 122 may include pixels to emit light of apredominant color such as red, green, blue, white, or yellow. In someimplementations, display electronics 122 may display a three-dimensional(3D) image through stereoscopic effects produced by two-dimensionalpanels to create a subjective perception of image depth. For example,display electronics 122 may include a left display and a right displaypositioned in front of a user's left eye and right eye, respectively.The left and right displays may present copies of an image shiftedhorizontally relative to each other to create a stereoscopic effect(e.g., a perception of image depth by a user viewing the image).

In certain embodiments, display optics 124 may display image contentoptically (e.g., using optical waveguides and couplers) or magnify imagelight received from display electronics 122, correct optical errorsassociated with the image light, and present the corrected image lightto a user of near-eye display 120. In various embodiments, displayoptics 124 may include one or more optical elements, such as, forexample, a substrate, optical waveguides, an aperture, a Fresnel lens, aconvex lens, a concave lens, a filter, input/output couplers, or anyother suitable optical elements that may affect image light emitted fromdisplay electronics 122. Display optics 124 may include a combination ofdifferent optical elements as well as mechanical couplings to maintainrelative spacing and orientation of the optical elements in thecombination. One or more optical elements in display optics 124 may havean optical coating, such as an anti-reflective coating, a reflectivecoating, a filtering coating, or a combination of different opticalcoatings.

Magnification of the image light by display optics 124 may allow displayelectronics 122 to be physically smaller, weigh less, and consume lesspower than larger displays. Additionally, magnification may increase afield of view of the displayed content. The amount of magnification ofimage light by display optics 124 may be changed by adjusting, adding,or removing optical elements from display optics 124. In someembodiments, display optics 124 may project displayed images to one ormore image planes that may be further away from the user's eyes thannear-eye display 120.

Display optics 124 may also be designed to correct one or more types ofoptical errors, such as two-dimensional optical errors,three-dimensional optical errors, or any combination thereof.Two-dimensional errors may include optical aberrations that occur in twodimensions. Example types of two-dimensional errors may include barreldistortion, pincushion distortion, longitudinal chromatic aberration,and transverse chromatic aberration. Three-dimensional errors mayinclude optical errors that occur in three dimensions. Example types ofthree-dimensional errors may include spherical aberration, comaticaberration, field curvature, and astigmatism.

Locators 126 may be objects located in specific positions on near-eyedisplay 120 relative to one another and relative to a reference point onnear-eye display 120. In some implementations, console 110 may identifylocators 126 in images captured by external imaging device 150 todetermine the artificial reality headset's position, orientation, orboth. A locator 126 may be an LED, a corner cube reflector, a reflectivemarker, a type of light source that contrasts with an environment inwhich near-eye display 120 operates, or any combination thereof. Inembodiments where locators 126 are active components (e.g., LEDs orother types of light emitting devices), locators 126 may emit light inthe visible band (e.g., about 380 nm to 750 nm), in the infrared (IR)band (e.g., about 750 nm to 1 mm), in the ultraviolet band (e.g., about10 nm to about 380 nm), in another portion of the electromagneticspectrum, or in any combination of portions of the electromagneticspectrum.

External imaging device 150 may include one or more cameras, one or morevideo cameras, any other device capable of capturing images includingone or more of locators 126, or any combination thereof. Additionally,external imaging device 150 may include one or more filters (e.g., toincrease signal to noise ratio). External imaging device 150 may beconfigured to detect light emitted or reflected from locators 126 in afield of view of external imaging device 150. In embodiments wherelocators 126 include passive elements (e.g., retroreflectors), externalimaging device 150 may include a light source that illuminates some orall of locators 126, which may retro-reflect the light to the lightsource in external imaging device 150. Slow calibration data may becommunicated from external imaging device 150 to console 110, andexternal imaging device 150 may receive one or more calibrationparameters from console 110 to adjust one or more imaging parameters(e.g., focal length, focus, frame rate, sensor temperature, shutterspeed, aperture, etc.).

Position sensors 128 may generate one or more measurement signals inresponse to motion of near-eye display 120. Examples of position sensors128 may include accelerometers, gyroscopes, magnetometers, othermotion-detecting or error-correcting sensors, or any combinationthereof. For example, in some embodiments, position sensors 128 mayinclude multiple accelerometers to measure translational motion (e.g.,forward/back, up/down, or left/right) and multiple gyroscopes to measurerotational motion (e.g., pitch, yaw, or roll). In some embodiments,various position sensors may be oriented orthogonally to each other.

IMU 132 may be an electronic device that generates fast calibration databased on measurement signals received from one or more of positionsensors 128. Position sensors 128 may be located external to IMU 132,internal to IMU 132, or any combination thereof. Based on the one ormore measurement signals from one or more position sensors 128, IMU 132may generate fast calibration data indicating an estimated position ofnear-eye display 120 relative to an initial position of near-eye display120. For example, IMU 132 may integrate measurement signals receivedfrom accelerometers over time to estimate a velocity vector andintegrate the velocity vector over time to determine an estimatedposition of a reference point on near-eye display 120. Alternatively,IMU 132 may provide the sampled measurement signals to console 110,which may determine the fast calibration data. While the reference pointmay generally be defined as a point in space, in various embodiments,the reference point may also be defined as a point within near-eyedisplay 120 (e.g., a center of IMU 132).

Eye-tracking unit 130 may include one or more eye-tracking systems. Eyetracking may refer to determining an eye's position, includingorientation and location of the eye, relative to near-eye display 120.An eye-tracking system may include an imaging system to image one ormore eyes and may optionally include a light emitter, which may generatelight that is directed to an eye such that light reflected by the eyemay be captured by the imaging system. For example, eye-tracking unit130 may include a non-coherent or coherent light source (e.g., a laserdiode) emitting light in the visible spectrum or infrared spectrum, anda camera capturing the light reflected by the user's eye. As anotherexample, eye-tracking unit 130 may capture reflected radio waves emittedby a miniature radar unit. Eye-tracking unit 130 may use low-power lightemitters that emit light at frequencies and intensities that would notinjure the eye or cause physical discomfort. Eye-tracking unit 130 maybe arranged to increase contrast in images of an eye captured byeye-tracking unit 130 while reducing the overall power consumed byeye-tracking unit 130 (e.g., reducing power consumed by a light emitterand an imaging system included in eye-tracking unit 130). For example,in some implementations, eye-tracking unit 130 may consume less than 100milliwatts of power.

Near-eye display 120 may use the orientation of the eye to, e.g.,determine an inter-pupillary distance (IPD) of the user, determine gazedirection, introduce depth cues (e.g., blur image outside of the user'smain line of sight), collect heuristics on the user interaction in theVR media (e.g., time spent on any particular subject, object, or frameas a function of exposed stimuli), some other functions that are basedin part on the orientation of at least one of the user's eyes, or anycombination thereof. Because the orientation may be determined for botheyes of the user, eye-tracking unit 130 may be able to determine wherethe user is looking. For example, determining a direction of a user'sgaze may include determining a point of convergence based on thedetermined orientations of the user's left and right eyes. A point ofconvergence may be the point where the two foveal axes of the user'seyes intersect. The direction of the user's gaze may be the direction ofa line passing through the point of convergence and the mid-pointbetween the pupils of the user's eyes.

Input/output interface 140 may be a device that allows a user to sendaction requests to console 110. An action request may be a request toperform a particular action. For example, an action request may be tostart or to end an application or to perform a particular action withinthe application. Input/output interface 140 may include one or moreinput devices. Example input devices may include a keyboard, a mouse, agame controller, a glove, a button, a touch screen, or any othersuitable device for receiving action requests and communicating thereceived action requests to console 110. An action request received bythe input/output interface 140 may be communicated to console 110, whichmay perform an action corresponding to the requested action. In someembodiments, input/output interface 140 may provide haptic feedback tothe user in accordance with instructions received from console 110. Forexample, input/output interface 140 may provide haptic feedback when anaction request is received, or when console 110 has performed arequested action and communicates instructions to input/output interface140. In some embodiments, external imaging device 150 may be used totrack input/output interface 140, such as tracking the location orposition of a controller (which may include, for example, an IR lightsource) or a hand of the user to determine the motion of the user. Insome embodiments, near-eye display 120 may include one or more imagingdevices to track input/output interface 140, such as tracking thelocation or position of a controller or a hand of the user to determinethe motion of the user.

Console 110 may provide content to near-eye display 120 for presentationto the user in accordance with information received from one or more ofexternal imaging device 150, near-eye display 120, and input/outputinterface 140. In the example shown in FIG. 1, console 110 may includean application store 112, a headset tracking module 114, an artificialreality engine 116, and an eye-tracking module 118. Some embodiments ofconsole 110 may include different or additional modules than thosedescribed in conjunction with FIG. 1. Functions further described belowmay be distributed among components of console 110 in a different mannerthan is described here.

In some embodiments, console 110 may include a processor and anon-transitory computer-readable storage medium storing instructionsexecutable by the processor. The processor may include multipleprocessing units executing instructions in parallel. The non-transitorycomputer-readable storage medium may be any memory, such as a hard diskdrive, a removable memory, or a solid-state drive (e.g., flash memory ordynamic random access memory (DRAM)). In various embodiments, themodules of console 110 described in conjunction with FIG. 1 may beencoded as instructions in the non-transitory computer-readable storagemedium that, when executed by the processor, cause the processor toperform the functions further described below.

Application store 112 may store one or more applications for executionby console 110. An application may include a group of instructions that,when executed by a processor, generates content for presentation to theuser. Content generated by an application may be in response to inputsreceived from the user via movement of the user's eyes or inputsreceived from the input/output interface 140. Examples of theapplications may include gaming applications, conferencing applications,video playback application, or other suitable applications.

Headset tracking module 114 may track movements of near-eye display 120using slow calibration information from external imaging device 150. Forexample, headset tracking module 114 may determine positions of areference point of near-eye display 120 using observed locators from theslow calibration information and a model of near-eye display 120.Headset tracking module 114 may also determine positions of a referencepoint of near-eye display 120 using position information from the fastcalibration information. Additionally, in some embodiments, headsettracking module 114 may use portions of the fast calibrationinformation, the slow calibration information, or any combinationthereof, to predict a future location of near-eye display 120. Headsettracking module 114 may provide the estimated or predicted futureposition of near-eye display 120 to artificial reality engine 116.

Artificial reality engine 116 may execute applications within artificialreality system environment 100 and receive position information ofnear-eye display 120, acceleration information of near-eye display 120,velocity information of near-eye display 120, predicted future positionsof near-eye display 120, or any combination thereof from headsettracking module 114. Artificial reality engine 116 may also receiveestimated eye position and orientation information from eye-trackingmodule 118. Based on the received information, artificial reality engine116 may determine content to provide to near-eye display 120 forpresentation to the user. For example, if the received informationindicates that the user has looked to the left, artificial realityengine 116 may generate content for near-eye display 120 that mirrorsthe user's eye movement in a virtual environment. Additionally,artificial reality engine 116 may perform an action within anapplication executing on console 110 in response to an action requestreceived from input/output interface 140, and provide feedback to theuser indicating that the action has been performed. The feedback may bevisual or audible feedback via near-eye display 120 or haptic feedbackvia input/output interface 140.

Eye-tracking module 118 may receive eye-tracking data from eye-trackingunit 130 and determine the position of the user's eye based on the eyetracking data. The position of the eye may include an eye's orientation,location, or both relative to near-eye display 120 or any elementthereof. Because the eye's axes of rotation change as a function of theeye's location in its socket, determining the eye's location in itssocket may allow eye-tracking module 118 to more accurately determinethe eye's orientation.

FIG. 2 is a perspective view of an example of a near-eye display in theform of an HMD device 200 for implementing some of the examplesdisclosed herein. HMD device 200 may be a part of, e.g., a VR system, anAR system, an MR system, or any combination thereof. HMD device 200 mayinclude a body 220 and a head strap 230. FIG. 2 shows a bottom side 223,a front side 225, and a left side 227 of body 220 in the perspectiveview. Head strap 230 may have an adjustable or extendible length. Theremay be a sufficient space between body 220 and head strap 230 of HMDdevice 200 for allowing a user to mount HMD device 200 onto the user'shead. In various embodiments, HMD device 200 may include additional,fewer, or different components. For example, in some embodiments, HMDdevice 200 may include eyeglass temples and temple tips as shown in, forexample, FIG. 3 below, rather than head strap 230.

HMD device 200 may present to a user media including virtual and/oraugmented views of a physical, real-world environment withcomputer-generated elements. Examples of the media presented by HMDdevice 200 may include images (e.g., two-dimensional (2D) orthree-dimensional (3D) images), videos (e.g., 2D or 3D videos), audio,or any combination thereof. The images and videos may be presented toeach eye of the user by one or more display assemblies (not shown inFIG. 2) enclosed in body 220 of HMD device 200. In various embodiments,the one or more display assemblies may include a single electronicdisplay panel or multiple electronic display panels (e.g., one displaypanel for each eye of the user). Examples of the electronic displaypanel(s) may include, for example, an LCD, an OLED display, an ILEDdisplay, a μLED display, an AMOLED, a TOLED, some other display, or anycombination thereof. HMD device 200 may include two eyebox regions.

In some implementations, HMD device 200 may include various sensors (notshown), such as depth sensors, motion sensors, position sensors, and eyetracking sensors. Some of these sensors may use a structured lightpattern for sensing. In some implementations, HMD device 200 may includean input/output interface for communicating with a console. In someimplementations, HMD device 200 may include a virtual reality engine(not shown) that can execute applications within HMD device 200 andreceive depth information, position information, accelerationinformation, velocity information, predicted future positions, or anycombination thereof of HMD device 200 from the various sensors. In someimplementations, the information received by the virtual reality enginemay be used for producing a signal (e.g., display instructions) to theone or more display assemblies. In some implementations, HMD device 200may include locators (not shown, such as locators 126) located in fixedpositions on body 220 relative to one another and relative to areference point. Each of the locators may emit light that is detectableby an external imaging device.

FIG. 3 is a perspective view of an example of a near-eye display 300 inthe form of a pair of glasses for implementing some of the examplesdisclosed herein. Near-eye display 300 may be a specific implementationof near-eye display 120 of FIG. 1, and may be configured to operate as avirtual reality display, an augmented reality display, and/or a mixedreality display. Near-eye display 300 may include a frame 305 and adisplay 310. Display 310 may be configured to present content to a user.In some embodiments, display 310 may include display electronics and/ordisplay optics. For example, as described above with respect to near-eyedisplay 120 of FIG. 1, display 310 may include an LCD display panel, anLED display panel, or an optical display panel (e.g., a waveguidedisplay assembly).

Near-eye display 300 may further include various sensors 350 a, 350 b,350 c, 350 d, and 350 e on or within frame 305. In some embodiments,sensors 350 a-350 e may include one or more depth sensors, motionsensors, position sensors, inertial sensors, or ambient light sensors.In some embodiments, sensors 350 a-350 e may include one or more imagesensors configured to generate image data representing different fieldsof views in different directions. In some embodiments, sensors 350 a-350e may be used as input devices to control or influence the displayedcontent of near-eye display 300, and/or to provide an interactiveVR/AR/MR experience to a user of near-eye display 300. In someembodiments, sensors 350 a-350 e may also be used for stereoscopicimaging.

In some embodiments, near-eye display 300 may further include one ormore illuminators 330 to project light into the physical environment.The projected light may be associated with different frequency bands(e.g., visible light, infra-red light, ultra-violet light, etc.), andmay serve various purposes. For example, illuminator(s) 330 may projectlight in a dark environment (or in an environment with low intensity ofinfra-red light, ultra-violet light, etc.) to assist sensors 350 a-350 ein capturing images of different objects within the dark environment. Insome embodiments, illuminator(s) 330 may be used to project certainlight pattern onto the objects within the environment. In someembodiments, illuminator(s) 330 may be used as locators, such aslocators 126 described above with respect to FIG. 1.

In some embodiments, near-eye display 300 may also include ahigh-resolution camera 340. Camera 340 may capture images of thephysical environment in the field of view. The captured images may beprocessed, for example, by a virtual reality engine (e.g., artificialreality engine 116 of FIG. 1) to add virtual objects to the capturedimages or modify physical objects in the captured images, and theprocessed images may be displayed to the user by display 310 for AR orMR applications.

FIG. 4 is a simplified diagram illustrating an example of an opticalsystem 400 in a near-eye display system. Optical system 400 may includean image source 410 and projector optics 420. In the example shown inFIG. 4, image source 410 is in front of projector optics 420. In variousembodiments, image source 410 may be located outside of the field ofview of user's eye 490. For example, one or more reflectors ordirectional couplers may be used to deflect light from an image sourcethat is outside of the field of view of user's eye 490 to make the imagesource appear to be at the location of image source 410 shown in FIG. 4.Light from an area (e.g., a pixel or a light emitting device) on imagesource 410 may be collimated and directed to an exit pupil 430 byprojector optics 420. Thus, objects at different spatial locations onimage source 410 may appear to be objects far away from user's eye 490in different viewing angles (FOVs). The collimated light from differentviewing angles may then be focused by the lens of user's eye 490 ontodifferent locations on retina 492 of user's eye 490. For example, atleast some portions of the light may be focused on a fovea 494 on retina492. Collimated light rays from an area on image source 410 and incidenton user's eye 490 from a same direction may be focused onto a samelocation on retina 492. As such, a single image of image source 410 maybe formed on retina 492.

The user experience of using an artificial reality system may depend onseveral characteristics of the optical system, including field of view(FOV), image quality (e.g., angular resolution), size of the eyebox (toaccommodate for eye and head movements), and brightness of the light (orcontrast) within the eyebox. Field of view describes the angular rangeof the image as seen by the user, usually measured in degrees asobserved by one eye (for a monocular HMD) or both eyes (for eitherbiocular or binocular HMDs). The human visual system may have a totalbinocular FOV of about 200° (horizontal) by 130° (vertical). To create afully immersive visual environment, a large FOV is desirable because alarge FOV (e.g., greater than about 60°) may provide a sense of “beingin” an image, rather than merely viewing the image. Smaller fields ofview may also preclude some important visual information. For example,an HMD system with a small FOV may use a gesture interface, but theusers may not see their hands in the small FOV to be sure that they areusing the correct motions. On the other hand, wider fields of view mayrequire larger displays or optical systems, which may influence thesize, weight, cost, and comfort of using the HMD.

Resolution may refer to the angular size of a displayed pixel or imageelement appearing to a user, or the ability for the user to view andcorrectly interpret an object as imaged by a pixel and/or other pixels.The resolution of an HMD may be specified as the number of pixels on theimage source for a given FOV value, from which an angular resolution maybe determined by dividing the FOV in one direction by the number ofpixels in the same direction on the image source. For example, for ahorizontal FOV of 40° and 1080 pixels in the horizontal direction on theimage source, the corresponding angular resolution may be about 2.2arcminutes, compared with the one-arc-minute resolution associated withSnellen 20/20 human visual acuity.

In some cases, the eyebox may be a two-dimensional box in front of theuser's eye, from which the displayed image from the image source may beviewed. If the pupil of the user moves outside of the eyebox, thedisplayed image may not be seen by the user. For example, in anon-pupil-forming configuration, there exists a viewing eyebox withinwhich there will be unvignetted viewing of the HMD image source, and thedisplayed image may vignette or may be clipped but may still be viewablewhen the pupil of user's eye is outside of the viewing eyebox. In apupil-forming configuration, the image may not be viewable outside theexit pupil.

The fovea of a human eye, where the highest resolution may be achievedon the retina, may correspond to an FOV of about 2° to about 3°. Thismay require that the eye rotates in order to view off-axis objects witha highest resolution. The rotation of the eye to view the off-axisobjects may introduce a translation of the pupil because the eye rotatesaround a point that is about 10 mm behind the pupil. In addition, a usermay not always be able to accurately position the pupil (e.g., having aradius of about 2.5 mm) of the user's eye at an ideal location in theeyebox. Furthermore, the environment where the HMD is used may requirethe eyebox to be larger to allow for movement of the user's eye and/orhead relative the HMD, for example, when the HMD is used in a movingvehicle or designed to be used while the user is moving on foot. Theamount of movement in these situations may depend on how well the HMD iscoupled to the user's head.

Thus, the optical system of the HMD may need to provide a sufficientlylarge exit pupil or viewing eyebox for viewing the full FOV with fullresolution, in order to accommodate the movements of the user's pupilrelative to the HMD. For example, in a pupil-forming configuration, aminimum size of 12 mm to 15 mm may be desired for the exit pupil. If theeyebox is too small, minor misalignments between the eye and the HMD mayresult in at least partial loss of the image, and the user experiencemay be substantially impaired. In general, the lateral extent of theeyebox is more critical than the vertical extent of the eyebox. This maybe in part due to the significant variances in eye separation distancebetween users, and the fact that misalignments to eyewear tend to morefrequently occur in the lateral dimension and users tend to morefrequently adjust their gaze left and right, and with greater amplitude,than adjusting the gaze up and down. Thus, techniques that can increasethe lateral dimension of the eyebox may substantially improve a user'sexperience with an HMD. On the other hand, the larger the eyebox, thelarger the optics and the heavier and bulkier the near-eye displaydevice may be.

In order to view the displayed image against a bright background, theimage source of an AR HMD may need to be sufficiently bright, and theoptical system may need to be efficient to provide a bright image to theuser's eye such that the displayed image may be visible in a backgroundincluding strong ambient light, such as sunlight. The optical system ofan HMD may be designed to concentrate light in the eyebox. When theeyebox is large, an image source with high power may be used to providea bright image viewable within the large eyebox. Thus, there may betrade-offs among the size of the eyebox, cost, brightness, opticalcomplexity, image quality, and size and weight of the optical system.

FIG. 5 illustrates an example of an optical see-through augmentedreality system 500 including a waveguide display for exit pupilexpansion according to certain embodiments. Augmented reality system 500may include a projector 510 and a combiner 515. Projector 510 mayinclude a light source or image source 512 and projector optics 514. Insome embodiments, light source or image source 512 may include one ormore micro-LED devices. In some embodiments, image source 512 mayinclude a plurality of pixels that displays virtual objects, such as anLCD display panel or an LED display panel. In some embodiments, imagesource 512 may include a light source that generates coherent orpartially coherent light. For example, image source 512 may include alaser diode, a vertical cavity surface emitting laser, an LED, asuperluminescent LED (sLED), and/or a micro-LED described above. In someembodiments, image source 512 may include a plurality of light sources(e.g., an array of micro-LEDs described above) each emitting amonochromatic image light corresponding to a primary color (e.g., red,green, or blue). In some embodiments, image source 512 may include threetwo-dimensional arrays of micro-LEDs, where each two-dimensional arrayof micro-LEDs may include micro-LEDs configured to emit light of aprimary color (e.g., red, green, or blue). In some embodiments, imagesource 512 may include an optical pattern generator, such as a spatiallight modulator. Projector optics 514 may include one or more opticalcomponents that can condition the light from image source 512, such asexpanding, collimating, scanning, or projecting light from image source512 to combiner 515. The one or more optical components may include, forexample, one or more lenses, liquid lenses, mirrors, free-form optics,apertures, and/or gratings. For example, in some embodiments, imagesource 512 may include one or more one-dimensional arrays or elongatedtwo-dimensional arrays of micro-LEDs, and projector optics 514 mayinclude one or more one-dimensional scanners (e.g., micro-mirrors orprisms) configured to scan the one-dimensional arrays or elongatedtwo-dimensional arrays of micro-LEDs to generate image frames. In someembodiments, projector optics 514 may include a liquid lens (e.g., aliquid crystal lens) with a plurality of electrodes that allows scanningof the light from image source 512.

Combiner 515 may include an input coupler 530 for coupling light fromprojector 510 into a substrate 520 of combiner 515. Input coupler 530may include a volume holographic grating or another diffractive opticalelement (DOE) (e.g., a surface-relief grating (SRG)), a slantedreflective surface of substrate 520, or a refractive coupler (e.g., awedge or a prism). For example, input coupler 530 may include areflection volume Bragg grating or a transmission volume Bragg grating.Input coupler 530 may have a coupling efficiency of greater than 30%,50%, 75%, 90%, or higher for visible light. Light coupled into substrate520 may propagate within substrate 520 through, for example, totalinternal reflection (TIR). Substrate 520 may be in the form of a lens ofa pair of eyeglasses. Substrate 520 may have a flat or a curved surface,and may include one or more types of dielectric materials, such asglass, quartz, plastic, polymer, poly(methyl methacrylate) (PMMA),crystal, ceramic, or the like. A thickness of the substrate may rangefrom, for example, less than about 1 mm to about 10 mm or more.Substrate 520 may be transparent to visible light.

Substrate 520 may include or may be coupled to a plurality of outputcouplers 540 each configured to extract at least a portion of the lightguided by and propagating within substrate 520 from substrate 520, anddirect extracted light 560 to an eyebox 595 where an eye 590 of the userof augmented reality system 500 may be located when augmented realitysystem 500 is in use. The plurality of output couplers 540 may replicatethe exit pupil to increase the size of eyebox 595, such that thedisplayed image may be visible in a larger area. As input coupler 530,output couplers 540 may include grating couplers (e.g., volumeholographic gratings or surface-relief gratings), other diffractionoptical elements (DOEs), prisms, etc. For example, output couplers 540may include reflection volume Bragg gratings or transmission volumeBragg gratings. Output couplers 540 may have different coupling (e.g.,diffraction) efficiencies at different locations. Substrate 520 may alsoallow light 550 from the environment in front of combiner 515 to passthrough with little or no loss. Output couplers 540 may also allow light550 to pass through with little loss. For example, in someimplementations, output couplers 540 may have a very low diffractionefficiency for light 550 such that light 550 may be refracted orotherwise pass through output couplers 540 with little loss, and thusmay have a higher intensity than extracted light 560. In someimplementations, output couplers 540 may have a high diffractionefficiency for light 550 and may diffract light 550 in certain desireddirections (i.e., diffraction angles) with little loss. As a result, theuser may be able to view combined images of the environment in front ofcombiner 515 and images of virtual objects projected by projector 510.In some implementations, output couplers 540 may have a high diffractionefficiency for light 550 and may diffract light 550 to certain desireddirections (e.g., diffraction angles) with little loss.

In some embodiments, projector 510, input coupler 530, and outputcoupler 540 may be on any side of substrate 520. Input coupler 530 andoutput coupler 540 may be reflective gratings (also referred to asreflection gratings) or transmissive gratings (also referred to astransmission gratings) to couple display light into or out of substrate520.

FIG. 6 illustrates an example of an optical see-through augmentedreality system 600 including a waveguide display for exit pupilexpansion according to certain embodiments. Augmented reality system 600may be similar to augmented reality system 500, and may include thewaveguide display and a projector that may include a light source orimage source 612 and projector optics 614. The waveguide display mayinclude a substrate 630, an input coupler 640, and a plurality of outputcouplers 650 as described above with respect to augmented reality system500. While FIG. 5 only shows the propagation of light from a singlefield of view, FIG. 6 shows the propagation of light from multiplefields of view.

FIG. 6 shows that the exit pupil is replicated by output couplers 650 toform an aggregated exit pupil or eyebox, where different fields of view(e.g., different pixels on image source 612) may be associated withdifferent respective propagation directions towards the eyebox, andlight from a same field of view (e.g., a same pixel on image source 612)may have a same propagation direction for the different individual exitpupils. Thus, a single image of image source 612 may be formed by theuser's eye located anywhere in the eyebox, where light from differentindividual exit pupils and propagating in the same direction may be froma same pixel on image source 612 and may be focused onto a same locationon the retina of the user's eye. FIG. 6 shows that the image of theimage source is visible by the user's eye even if the user's eye movesto different locations in the eyebox.

In many waveguide-based near-eye display systems, in order to expand theeyebox of the waveguide-based near-eye display in two dimensions, two ormore output gratings may be used to expand the display light in twodimensions or along two axes (which may be referred to as dual-axispupil expansion). The two gratings may have different gratingparameters, such that one grating may be used to replicate the exitpupil in one direction and the other grating may be used to replicatethe exit pupil in another direction.

As described above, the input and output grating couplers describedabove can be volume holographic gratings or surface-relief gratings,which may have very different Klein-Cook parameter Q:

${Q = \frac{2{\pi\lambda d}}{n\Lambda^{2}}},$where d is the thickness of the grating, A is the wavelength of theincident light in free space, A is the grating period, and n is therefractive index of the recording medium. The Klein-Cook parameter Q maydivide light diffraction by gratings into three regimes. When a gratingis characterized by Q<<1, light diffraction by the grating may bereferred to as Raman-Nath diffraction, where multiple diffraction ordersmay occur for normal and/or oblique incident light. When a grating ischaracterized by Q>>1 (e.g., Q≥10), light diffraction by the grating maybe referred to as Bragg diffraction, where generally only the zeroth andthe ±1 diffraction orders may occur for light incident on the grating atan angle satisfying the Bragg condition. When a grating is characterizedby Q≈1, the diffraction by the grating may be between the Raman-Nathdiffraction and the Bragg diffraction. To meet Bragg conditions, thethickness d of the grating may be higher than certain values to occupy avolume (rather than at a surface) of a medium, and thus may be referredto as a volume Bragg grating. VBGs may generally have relatively smallrefractive index modulations (e.g., Δn≤0.05) and high spectral andangular selectivity, while surface-relief gratings may generally havelarge refractive index modulations (e.g., Δn≥0.5) and wide spectral andangular bandwidths.

FIG. 7A illustrates the spectral bandwidth of an example of a volumeBragg grating (e.g., a reflection VBG) and the spectral bandwidth of anexample of a surface-relief grating (e.g., a transmissive SRG). Thehorizontal axis represents the wavelength of the incident visible lightand the vertical axis corresponds to the diffraction efficiency. Asshown by a curve 710, the diffraction efficiency of the reflection VBGis high in a narrow wavelength range, such as green light. In contrast,the diffraction efficiency of the transmissive SRG may be high in a verywide wavelength range, such as from blue to red light, as shown by acurve 720.

FIG. 7B illustrates the angular bandwidth of an example of a volumeBragg grating (e.g., a reflection VBG) and the angular bandwidth of anexample of a surface-relief grating (e.g., a transmissive SRG). Thehorizontal axis represents the incident angle of the visible lightincident on the grating, and the vertical axis corresponds to thediffraction efficiency. As shown by a curve 715, the diffractionefficiency of the reflection VBG is high for light incident on thegrating from a narrow angular range, such as about ±2.5° from theperfect Bragg condition. In contrast, the diffraction efficiency of thetransmissive SRG is high in a very wide angular range, such as greaterthan about ±10° or wider, as shown by a curve 725.

Due to the high spectral selectivity at the Bragg condition, VBGs, suchas reflection VBGs, may allow for single-waveguide design withoutcrosstalk between primary colors, and may exhibit superior see-throughquality. However, the spectral and angular selectivity may lead to lowerefficiency because only a portion of the display light in the full FOVmay be diffracted and reach user's eyes.

FIG. 8A illustrates an example of an optical see-through augmentedreality system including a waveguide display 800 and surface-reliefgratings for exit pupil expansion according to certain embodiments.Waveguide display 800 may include a substrate 810 (e.g., a waveguide),which may be similar to substrate 520. Substrate 810 may be transparentto visible light and may include, for example, a glass, quartz, plastic,polymer, PMMA, ceramic, or crystal substrate. Substrate 810 may be aflat substrate or a curved substrate. Substrate 810 may include a firstsurface 812 and a second surface 814. Display light may be coupled intosubstrate 810 by an input coupler 820, and may be reflected by firstsurface 812 and second surface 814 through total internal reflection,such that the display light may propagate within substrate 810. Asdescribed above, input coupler 820 may include a grating, a refractivecoupler (e.g., a wedge or a prism), or a reflective coupler (e.g., areflective surface having a slant angle with respect to substrate 810).For example, in one embodiment, input coupler 820 may include a prismthat may couple display light of different colors into substrate 810 ata same refraction angle. In another example, input coupler 820 mayinclude a grating coupler that may diffract light of different colorsinto substrate 810 at different directions. Input coupler 820 may have acoupling efficiency of greater than 10%, 20%, 30%, 50%, 75%, 90%, orhigher for visible light.

Waveguide display 800 may also include a first grating 830 and a secondgrating 840 positioned on one or two surfaces (e.g., first surface 812and second surface 814) of substrate 810 for expanding incident displaylight beam in two dimensions in order to fill an eyebox (or output orexit pupil) with the display light. First grating 830 may be configuredto expand at least a portion of the display light beam along onedirection, such as approximately in the x direction. Display lightcoupled into substrate 810 may propagate in a direction shown by a line832. While the display light propagates within substrate 810 along adirection shown by line 832, a portion of the display light may bediffracted by a portion of first grating 830 towards second grating 840as shown by a line 834 each time the display light propagating withinsubstrate 810 reaches first grating 830. Second grating 840 may thenexpand the display light from first grating 830 in a different direction(e.g., approximately in the y direction) by diffracting a portion of thedisplay light to the eyebox each time the display light propagatingwithin substrate 810 reaches second grating 840. On second grating 840,an exit region 850 represents the region where display light for thefull FOV at one pupil location in the eyebox (e.g., at the center theeyebox) may be coupled out of waveguide display 800

FIG. 8B illustrates an example of an eye box including two-dimensionalreplicated exit pupils. FIG. 8B shows that a single input pupil 805 maybe replicated by first grating 830 and second grating 840 to form anaggregated exit pupil 860 that includes a two-dimensional array ofindividual exit pupils 852. For example, the exit pupil may bereplicated in approximately the x direction by first grating 830 and inapproximately the y direction by second grating 840. As described above,output light from individual exit pupils 852 and propagating in a samedirection may be focused onto a same location in the retina of theuser's eye. Thus, a single image may be formed by the user's eye fromthe output light in the two-dimensional array of individual exit pupils852.

FIG. 9A illustrates wave vectors of light diffracted by examples ofsurface-relief gratings for exit pupil expansion in a waveguide displayand exit pupils for multiple colors. A circle 910 may represent wavevectors of light that may be guided by the waveguide. For light withwave vectors outside of circle 910, the light may become evanescent. Acircle 920 may represent wave vectors of light that may leak out of thewaveguide because the total-internal-reflection condition is not met.Thus, the ring between circle 910 and circle 920 may represent the wavevectors of light that can be guided by the waveguide and can propagatewithin the waveguide through TIR. Wave vectors 932 show the lightdispersion caused by the input grating, where light of different colorsmay have different wave vectors and different diffraction angles. Wavevectors 942 show the light dispersion caused by a front grating (e.g.,first grating 830), where light of different colors may have differentdiffraction angles. Wave vectors 952 show the light dispersion caused bya back grating (e.g., second grating 840), where light of differentcolors may have different diffraction angles. The wave vectors for eachcolor may form a respective closed triangle, and the triangles fordifferent colors may share a common origin vertex 922. Thus, the overalldispersion by the three gratings may be close to zero.

Even though the overall dispersion by the three gratings may be zero,the dispersion by each grating may cause the reduction or clipping ofthe field of view of the waveguide display due to the conditions underwhich light may be guided by the waveguide as shown by the ring betweencircle 910 and circle 920. For example, for a FOV 924, the footprints ofthe FOV after the diffraction by the input grating may be different fordifferent colors due to the dispersion by the input grating. In theexample shown in FIG. 9A, a footprint 936 of the FOV for light of afirst color may be located in the ring, while a portion of a footprint934 of the FOV for light of a second color and a portion of a footprint938 of the FOV for light of a third color may fall outside of the ringand thus may not be guided by the waveguide. In addition, the footprintsof the FOV after the diffraction by the front grating may be furtherclipped or reduced. In the example shown in FIG. 9A, a small portion ofa footprint 946 of the FOV for the light of the first color, a largeportion of a footprint 944 of the FOV for the light of the second color,and a large portion of a footprint 948 of the FOV for the light of thethird color may fall outside of the ring and thus may not be guided bythe waveguide and diffracted by the back grating to reach the exitpupil.

FIG. 9B illustrates the field-of-view clipping by the examples ofsurface-relief gratings for exit pupil expansion in the waveguidedisplay. For example, the FOV for the light of the first color after thediffraction by the back grating may be shown by a footprint 956, whichmay be close to the full FOV. For the light of the second color, a topportion of the FOV may be clipped after diffraction by the first gratingand a right portion of the FOV may be clipped after diffraction by thefront grating. Thus, the FOV for the light of the second color after thediffraction by the back grating may be shown by a footprint 954, whichmay be much smaller than the full FOV. Similarly, for the light of thethird color, a bottom portion of the FOV may be clipped afterdiffraction by the first grating and a left portion of the FOV may beclipped after diffraction by the front grating. Thus, the FOV for thelight of the third color after the diffraction by the back grating maybe shown by a footprint 958, which may be much smaller than the fullFOV. Thus, certain color components of the image may be missing forcertain fields of view. As such, in order to achieve the full FOV fordifferent colors, two or more waveguides and the corresponding gratingsmay be used. In addition, as described above, the wide bandwidth of SRGsmay cause crosstalk between light of different primary colors and/orfrom different FOVs, and thus multiple waveguides may also be used toavoid the crosstalk.

Due to the high spectral selectivity at the Bragg condition, VBGs, suchas reflection VBGs, may allow for single-waveguide design withoutcrosstalk between primary colors in a volume Bragg grating and mayachieve a superior see-through quality. Thus, input coupler 530 or 640and output coupler 540 or 650 may include a volume Bragg grating, whichmay be a volume hologram recorded in a holographic recording material byexposing the holographic recording material to light patterns generatedby the interference between two or more coherent light beams. In volumeBragg gratings, the incident angle and the wavelength of the incidentlight may need to satisfy the Bragg phase-matching condition in orderfor the incident light to be diffracted by the Bragg grating. When asingle Bragg grating is used in a waveguide-based near-eye display, thespectral and angular selectivity of the volume Bragg gratings may leadto lower efficiency because only a portion of the display light may bediffracted and reach user's eyes, and the field of view and the workingwavelength range of the waveguide-based near-eye display may be limited.In some embodiments, multiplexed VBGs may be used to improve theefficiency and increase the FOV.

FIG. 10A illustrates the front view of an example of a volume Bragggrating-based waveguide display 1000 according to certain embodiments.Waveguide display 1000 may include a substrate 1010, which may besimilar to substrate 520. Substrate 1010 may be transparent to visiblelight and may include, for example, a glass, quartz, plastic, polymer,PMMA, ceramic, or crystal substrate. Substrate 1010 may be a flatsubstrate or a curved substrate. Substrate 1010 may include a firstsurface 1012 and a second surface 1014. Display light may be coupledinto substrate 1010 by an input coupler 1020, and may be reflected byfirst surface 1012 and second surface 1014 through total internalreflection, such that the display light may propagate within substrate1010. As described above, input coupler 1020 may include a diffractivecoupler (e.g., a volume holographic grating or a surface-reliefgrating), a refractive coupler (e.g., a wedge or a prism), or areflective coupler (e.g., a reflective surface having a slant angle withrespect to substrate 1010). For example, in one embodiment, inputcoupler 1020 may include a prism that may couple display light ofdifferent colors into substrate 1010 at a same refraction angle. Inanother example, the input coupler may include a grating coupler thatmay diffract light of different colors into substrate 1010 at differentdirections.

Waveguide display 1000 may also include a first grating 1030 and asecond grating 1040 positioned on one or two surfaces (e.g., firstsurface 1012 and second surface 1014) of substrate 1010 for expandingincident display light beam in two dimensions in order to fill an eyeboxwith the display light. First grating 1030 may include one or moremultiplexed volume Bragg gratings each configured to expand at least aportion of the display light beam (e.g., light corresponding to acertain field of view and/or a wavelength range) along one direction, asshown by lines 1032, 1034, and 1036. For example, while the displaylight propagates within substrate 1010 along a direction shown by line1032, 1034, or 1036, a portion of the display light may be diffracted byfirst grating 1030 to second grating 1040 each time the display lightpropagating within substrate 1010 reaches first grating 1030. Secondgrating 1040 may then expand the display light from first grating 1030in a different direction by diffracting a portion of the display lightto the eyebox each time the display light propagating within substrate1010 reaches second grating 1040. On second grating 1040, an exit region1050 represents the region where display light for the full FOV at onepupil location in the eyebox (e.g., at the center the eyebox) may becoupled out of waveguide display 1000.

As described above, first grating 1030 and second grating 1040 may eachinclude a multiplexed VBG that includes multiple VBGs each designed fora specific FOV range and/or wavelength range. For example, first grating1030 may include a few hundred or more VBGs (e.g., about 300 to about1000 VBGs) recorded by a few hundred or more exposures, where each VBGmay be recorded under a different condition. Second grating 1040 mayalso include tens or hundreds of VBGs (e.g., 50 or more VBGs) recordedby tens or hundreds of exposures. First grating 1030 and second grating1040 may each be a transmission grating or a reflection grating.

FIGS. 10B and 10C illustrate the top and side views of volume Bragggrating-based waveguide display 1000, respectively. Input coupler 1020may include projector optics (not shown, e.g., a lens) and a prism.Display light may be collimated and projected onto the prism by theprojector optics, and may be coupled into substrate 1010 by the prism.The prism may have a refractive index that matches the refractive indexof substrate 1010 and may include a wedge having a certain angle suchthat light coupled into substrate 1010 may be incident on surface 1012or 1014 of substrate 1010 at an incident angle greater than the criticalangle for substrate 1010. As such, display light coupled into substrate1010 may be guided by substrate 1010 through total internal reflection,and may be diffracted by multiple regions of first grating 1030 towardssecond grating 1040 as described above. Second grating 1040 may thendiffract the display light out of substrate 1010 at multiple regions toreplicate the exit pupil.

FIG. 11 illustrates light dispersion in an example of a volume Bragggrating-based waveguide display, such as waveguide display 1000,according to certain embodiments. As shown in the example, a sphere 1110may represent wave vectors of light that may be guided by the waveguide.For light with wave vectors outside of sphere 1110, the light may becomeevanescent. A cone 1120 may represent wave vectors of light that mayleak out of the waveguide because the total-internal-reflectioncondition is not met. Thus, the region of sphere 1110 outside of cone1120 may represent the wave vectors of light that can be guided by thewaveguide and can propagate within the waveguide through TIR. Point 1130may represent the wave vector of the display light coupled into thewaveguide by, for example, a prism. Wave vectors 1140 show the lightdispersion caused by first grating 1030, where light of different colorsmay have different diffraction angles. Wave vectors 1150 show the lightdispersion caused by second grating 1040, where light of differentcolors may have different diffraction angles. Thus, the light coupledout of the substrate may have some dispersion, such that the images ofdifferent colors may not perfectly overlap with each other to form oneimage. Therefore, the displayed image may be blurred and the resolutionof the displayed image may be reduced.

FIG. 12A illustrates an example of a volume Bragg grating 1200. VolumeBragg grating 1200 shown in FIG. 12A may include a transmissionholographic grating that has a thickness D. The refractive index n ofvolume Bragg grating 1200 may be modulated at an amplitude Δn, and thegrating period of volume Bragg grating 1200 may be Λ. Incident light1210 having a wavelength λ may be incident on volume Bragg grating 1200at an incident angle θ, and may be refracted into volume Bragg grating1200 as incident light 1220 that propagates at an angle θ_(n) in volumeBragg grating 1200. Incident light 1220 may be diffracted by volumeBragg grating 1200 into diffraction light 1230, which may propagate at adiffraction angle θ_(d) in volume Bragg grating 1200 and may berefracted out of volume Bragg grating 1200 as diffraction light 1240.

FIG. 12B illustrates the Bragg condition for volume Bragg grating 1200shown in FIG. 12A. Volume Bragg grating 1200 may be a transmissiongrating. A vector 1205 may represent the grating vector {right arrowover (G)}, where |{right arrow over (G)}|=2π/Λ. A vector 1225 mayrepresent the incident wave vector {right arrow over (k_(i))}, and avector 1235 may represent the diffract wave vector {right arrow over(k_(d))}, where |{right arrow over (k_(i))}|=|{right arrow over(k_(d))}|=2πn/λ. Under the Bragg phase-matching condition, {right arrowover (k_(i))}−−{right arrow over (k_(d))}={right arrow over (G)}. Thus,for a given wavelength λ, there may only be one pair of incident angle θ(or θ_(n)) and diffraction angle θ_(d) that meets the Bragg conditionperfectly. Similarly, for a given incident angle θ, there may be onewavelength λ that meets the Bragg condition perfectly. As such, thediffraction may occur for a small wavelength range and in a smallincident angular range around a perfect Bragg condition. The diffractionefficiency, the wavelength selectivity, and the angular selectivity ofvolume Bragg grating 1200 may be functions of thickness D of volumeBragg grating 1200. For example, the full-width-half-magnitude (FWHM)wavelength range and the FWHM angular range of volume Bragg grating 1200around the Bragg condition may be inversely proportional to thickness Dof volume Bragg grating 1200, while the maximum diffraction efficiencyat the Bragg condition may be a function of sin²(a×Δn×D), where a is acoefficient. For a reflection volume Bragg grating, the maximumdiffraction efficiency at the Bragg condition may be a function oftanh²(a×Δn×D).

As described above, in some designs, in order to achieve a large FOV(e.g., larger than ±30°) and diffract light of different colors,multiple polymer layers each including a Bragg grating for a differentcolor (e.g., R, G, or B) and/or a different FOV may be arranged in astack for coupling the display light to the user's eyes. In somedesigns, a multiplexed Bragg grating may be used, where each part of themultiplexed Bragg grating may be used to diffract light in a differentFOV range and/or within a different wavelength range. Thus, in somedesigns, in order to achieve a desired diffraction efficiency and alarge FOV for the full visible spectrum (e.g., from about 400 nm toabout 700 nm, or from about 450 nm to about 650 nm), one or more thickvolume Bragg gratings each including a large number of gratings (orholograms) recorded by a large number of exposures (e.g., holographicrecordings), such as a few hundred or more than 1000, may be used.

VBGs or other holographic optical elements described above may berecorded in a holographic material (e.g., photopolymer) layer. In someembodiments, the VBGs can be recorded first and then laminated on asubstrate in a near-eye display system. In some embodiments, aholographic material layer may be coated or laminated on the substrateand the VBGs may then be recorded in the holographic material layer.

In general, to record a holographic optical element in a photosensitivematerial layer, two coherent beams may interfere with each other atcertain angles to generate a unique interference pattern in thephotosensitive material layer, which may in turn generate a uniquerefractive index modulation pattern in the photosensitive materiallayer, where the refractive index modulation pattern may correspond tothe light intensity pattern of the interference pattern. Thephotosensitive material layer may include, for example, silver halideemulsion, dichromated gelatin, photopolymers includingphoto-polymerizable monomers suspended in a polymer matrix,photorefractive crystals, and the like. One example of thephotosensitive material layer for holographic recording is two-stagephotopolymers that may include matrix precursors that can be pre-curedto form polymeric binders before holographic recording and writingmonomers for holographic recording.

In one example, the photosensitive material layer may include polymericbinders, monomers (e.g., acrylic monomers), and initiating agents, suchas initiators, chain transfer agents, or photosensitizing dyes. Thepolymeric binders may act as the support matrix. The monomers may bedispersed in the support matrix and may serve as refractive indexmodulators. The photosensitizing dyes may absorb light and interact withthe initiators to polymerize the monomers. Thus, in each exposure(recording), the interference pattern may cause the polymerization anddiffusion of the monomers to bright fringes, thus generatingconcentration and density gradients that may result in refractive indexmodulation. For example, areas with a higher concentration of monomersand polymerization may have a higher refractive index. As the exposureand polymerization proceed, fewer monomers may be available forpolymerization, and the diffusion may be suppressed. After all orsubstantially all monomers have been polymerized, no more new gratingsmay be recorded in the photosensitive material layer. In a thick VBGthat includes a large number of gratings recorded in a large number ofexposures, display haze may be significant.

As described above, in some waveguide-based near-eye display systems, inorder to expand the eyebox of the waveguide-based near-eye display, twooutput gratings (or two grating layers or two portions of a multiplexedgrating) may generally be used to expand the display light in twodimensions or along two axes for dual-axis pupil expansion. Spatiallyseparating the two output gratings and reducing the total number ofexposures for each output grating may help to reduce the display hazebecause the see-through region (e.g., the middle) of the waveguide-basednear-eye display may only include one output grating. For example, insome embodiments, the first output grating may be recorded with moreexposures (e.g., >500 or >1000 times) and may be positioned outside ofthe see-through region of the waveguide-based near-eye display. Thesecond output grating may be recorded with fewer exposures (e.g., <100or <50 times) and may be positioned in the see-through region of thewaveguide-based near-eye display. Thus, the display haze in thesee-through region may be significantly reduced. However, because of thespatial separation of the two output gratings, the overall size of thewaveguide-based near-eye display can be very large.

The grating couplers described above may include transmission VBGs orreflection VBGs, which may have some similar and some differentcharacteristics. For example, as described above, the FWHM wavelengthrange and the FWHM angular range of a transmissive or reflection volumeBragg grating near the Bragg condition may be inversely proportional tothickness D of the transmissive or reflection volume Bragg grating. Themaximum diffraction efficiency at the Bragg condition for a transmissionVBG may be a function of sin² (a×Δn×D), where a is a coefficient and Δnis the refractive index modulation, while the maximum diffractionefficiency at the Bragg condition for a reflection VBG may be a functionof tanh²(a×Δn×D). In addition, the parameters (e.g., the grating tiltangles) of the transmissive and reflection volume Bragg gratings may bedifferent in order to couple the display light into the waveguide atcertain angles such that the coupled display light can be guided by thewaveguide through TIR. Because of the different grating parameters, thedispersion characteristics of transmission gratings and reflectiongratings may be different.

FIG. 13A illustrates a front view of an example of a volume Bragggrating-based waveguide display 1300 with exit pupil expansion anddispersion reduction according to certain embodiments. FIG. 13Billustrates a side view of the example of volume Bragg grating-basedwaveguide display 1300 with exit pupil expansion and dispersionreduction according to certain embodiments. Waveguide display 1300 maybe similar to waveguide display 1000, and may include an input coupler1320 at a different location compared with input coupler 1020. Waveguidedisplay 1300 may include a substrate 1310, and a first grating 1330 anda second grating 1340 formed on or in substrate 1310. As input coupler1020, input coupler 1320 may include projector optics 1322 (e.g., alens) and a prism 1324. Display light may be coupled into substrate 1310by input coupler 1320 and may be guided by substrate 1310. The displaylight may reach a first portion 1332 of first grating 1330, and may bediffracted by first portion 1332 of first grating 1330 to change thepropagation direction and reach other portions of first grating 1330,which may each diffract the display light towards second grating 1340.Second grating 1340 may diffract the display light out of substrate 1310at different locations to form multiple exit pupils as described above.

First portion 1332 and each of other portions of first grating 1330 mayhave matching grating vectors (e.g., having a same grating vector in thex-y plane and having a same grating vector, opposite grating vectors, orboth the same and opposite grating vectors in the z direction, butrecorded in different exposure durations to achieve differentdiffraction efficiencies). Therefore, they may compensate for thedispersion of the display light by each other to reduce the overalldispersion, due to the opposite Bragg conditions (e.g., +1 order and −1order diffractions) of the diffractions at first portion 1332 and eachof other portions of first grating 1330. Therefore, the overalldispersion of the display light by waveguide display 1300 may be reducedin at least one direction.

FIG. 14A illustrates the propagation of light from different fields ofview in a reflection volume Bragg grating-based waveguide display 1400according to certain embodiments. Waveguide display 1400 may include areflection VBG 1410. Due to the grating tilt angle and thus the gratingvector of reflection VBG 1410, light from a positive field of view(shown by a line 1422) may have a smaller incident angle on fringes ofreflection VBG 1410 and also a smaller incident angle on the top surface1402 of waveguide display 1400. On the other hand, light from a negativefield of view (shown by a line 1424) may have a larger incident angle onthe fringes of reflection VBG 1410 and also a larger incident angle ontop surface 1402 of waveguide display 1400.

FIG. 14B illustrates the propagation of light from different fields ofview in a transmission volume Bragg grating-based waveguide display 1450according to certain embodiments. Waveguide display 1450 may include atransmission VBG 1460. Due to the grating tilt angle differences,transmission VBG 1460 may diffract light from different fields of viewin different manners compared with reflection VBG 1410. For example, asillustrated, light from a positive field of view (shown by a line 1472)may have a smaller incident angle on fringes of transmission VBG 1460but a larger incident angle on the bottom surface 1452 of waveguidedisplay 1450. On the other hand, light from a negative field of view(shown by a line 1474) may have a larger incident angle on the fringesof transmission VBG 1460 but a smaller incident angle on the bottomsurface 1452 of waveguide display 1450. The manner of diffraction oflight from different fields of view by a reflection or transmissiongrating may affect the form factor and performance of the waveguidedisplay.

FIG. 15 illustrates an example of a reflection volume Bragggrating-based waveguide display 1500 with exit pupil expansion anddispersion reduction according to certain embodiments. Waveguide display1500 may include a top grating 1505 and a bottom grating 1515. In theillustrated example, top grating 1505 may be a reflection VBG, andbottom grating 1515 may also be a reflection grating. On bottom grating1515, an exit region 1550 represents the region where display light forthe full FOV at one pupil location in the eyebox (e.g., at the centerthe eyebox) may be coupled out of the bottom grating. As shown in FIG.15, the top FOV at exit region 1550 represented by a line between a topright corner 1522 and a top left corner 1524 may map to a curve 1530 ontop grating 1505, where top right corner 1522 and top left corner 1524of exit region 1550 may map to a location 1532 and a location 1534 ontop grating 1505, respectively. The bottom FOV at exit region 1550represented by a line between a bottom right corner 1542 and a bottomleft corner 1544 may map to a curve 1510 on top grating 1505, wherebottom right corner 1542 and bottom left corner 1544 of exit region 1550may map to a location 1512 and a location 1514 on top grating 1505,respectively. Thus, if curve 1530 is below the line between top rightcorner 1522 and top left corner 1524 of exit region 1550, there may besome FOV clipping. As such, to preserve the full FOV, curve 1530 may beabove the line between top right corner 1522 and top left corner 1524 ofexit region 1550. Therefore, the size of waveguide display 1500 may belarge.

FIG. 16 illustrates an example of a transmission volume Bragggrating-based waveguide display 1600 with exit pupil expansion andform-factor reduction according to certain embodiments. Waveguidedisplay 1600 may include a top grating 1605 and a bottom grating 1615.In the illustrated example, top grating 1605 may be a reflection VBG,and bottom grating 1615 may be a transmission VBG. On bottom grating1615, an exit region 1650 represents the region where display light forthe full FOV at one pupil location in the eyebox (e.g., at the centerthe eyebox) may be coupled out of the bottom grating. As shown in FIG.16, the top FOV at exit region 1650 represented by a line between a topright corner 1622 and a top left corner 1624 may map to a curve 1610 ontop grating 1605, where top right corner 1622 and top left corner 1624of exit region 1650 may map to a location 1612 and a location 1614 ontop grating 1605, respectively. The bottom FOV at exit region 1650represented by a line between a bottom right corner 1642 and a bottomleft corner 1644 may map to a curve 1630 on top grating 1605, wherebottom right corner 1642 and bottom left corner 1644 of exit region 1650may map to a location 1632 and a location 1634 on top grating 1605,respectively. Thus, there can be some overlap between top grating 1605and bottom grating 1615 to reduce the overall size of waveguide display1600. For example, location 1632 may be lower than top right corner 1622and can still be mapped to bottom right corner 1642.

FIG. 17A illustrates an example of a transmission volume Bragg grating1700 in a waveguide display according to certain embodiments. Thegrating tilt angle α of transmission VBG 1700 may need to be within acertain range to transmissively diffract the display light. For example,if the grating tilt angle α of transmission VBG 1700 is lower than acertain value, transmission VBG 1700 may become a reflection VBG, thedistance between two consecutive locations where the display light mayreach the grating may be too large (and thus the exit pupil may besparsely replicated in the eyebox), or the display light may becomeevanescent. Thus, the grating tilt angle α of transmission VBG 1700needs to be greater than a certain value to transmissively diffract thedisplay light.

FIG. 17B illustrates an example of a transmission VBG 1710 in awaveguide display where light diffracted by the transmission VBG may notbe totally reflected and guided in the waveguide. The grating tilt angleα of transmission VBG 1710 may be greater than a certain value, such asgreater than about 60°. As such, light coupled into the waveguide may beincident on the surface of the waveguide at an incident angle less thanthe critical angle, and thus may not be totally reflected and guided inthe waveguide. Thus, the grating tilt angle α of a transmission VBG mayalso need to be lower than a certain value (e.g., about 60°) totransmissively diffract the display light into the waveguide such thatthe diffracted light may be guided by the waveguide through totalinternal reflection. As such, the grating tilt angle α of a transmissionVBG may need to be within a certain range.

FIG. 17C illustrates an example of a reflection volume Bragg grating1750 in a waveguide display according to certain embodiments. Thegrating tilt angle α of reflection VBG 1750 may also need to be within acertain range to reflectively diffract the display light. If the gratingtilt angle α of reflection VBG 1750 is greater than a certain value,reflection VBG 1750 may become a transmission VBG, the distance betweentwo consecutive locations where the display light may reach the gratingmay be too large (and thus the exit pupil may be sparsely replicated inthe eyebox), or the display light may become evanescent. Thus, thegrating tilt angle α of a reflection VBG may also need to be lower thana certain value to reflectively diffract the display light. In oneexample, the grating tilt angle α of reflection VBG 1750 may be about30°.

FIG. 17D illustrates an example of a reflection VBG 1760 in a waveguidedisplay where light diffracted by the reflection VBG is not totallyreflected and guided in the waveguide. The grating tilt angle α ofreflection VBG 1760 shown in FIG. 17D may be less than a certain value.As such, light coupled into the waveguide may be incident on the surfaceof the waveguide at an incident angle less than the critical angle, andthus may not be totally reflected and guided in the waveguide. Thegrating tilt angle α of reflection VBG 1760 may be less than about 30°.Thus, the grating tilt angle α of a reflection VBG may also need to begreater than a certain value. As such, the grating tilt angle α of areflection VBG may also need to be within a certain range toreflectively diffract the display light into the waveguide such that thediffracted light may be guided by the waveguide through total internalreflection. FIGS. 17A-17D show that the grating tilt angle α may besmaller for reflection gratings than for transmission gratings.

FIG. 18A illustrates the light dispersion by an example of a reflectionvolume Bragg grating 1800 in a waveguide display according to certainembodiments. Reflection VBG 1800 may be characterized by a gratingvector k_(g), a thickness d, and an average refractive index n. Thesurface normal direction of reflection VBG 1800 is N. The amount oflight dispersion by reflection VBG 1800 may be determined by:

${{\Delta\;\theta} = \frac{\lambda_{0}{{k_{g} \times N}}}{n \times d{{k_{g} \cdot k_{out}}}}},$where λ₀ is the wavelength of the light that perfectly meets the Braggcondition, and k_(out) is the wave vector of the light diffracted byreflection VBG 1800. When the grating tilt angle α of reflection VBG1800 is about 30°, the amount of light dispersion by reflection VBG 1800may be approximately:

${{\Delta\theta} \propto \frac{\sin\; 30^{\circ}}{d \times \cos\; 30^{\circ}}} = {\frac{{0.5}8}{d}.}$Thus, to achieve an angular resolution about 2 arcminutes, the thicknessd of reflection VBG 1800 may be at least about 0.5 mm.

FIG. 18B illustrates the light dispersion by an example of atransmission volume Bragg grating 1850 in a waveguide display accordingto certain embodiments. Transmission VBG 1850 may similarly becharacterized by a grating vector k_(g), a thickness d, and an averagerefractive index n. The surface normal direction of transmission VBG1850 is N. The amount of light dispersion by transmission VBG 1850 maybe determined by:

${{\Delta\;\theta} = \frac{\lambda_{0}{{k_{g} \times N}}}{n \times d{{k_{g} \cdot k_{out}}}}},$where λ₀ is the wavelength of the light that perfectly meets the Braggcondition, and k_(out) is the wave vector of the light diffracted bytransmission VBG 1850. When the grating tilt angle α of transmission VBG1850 is about 60°, the amount of light dispersion by transmission VBG1850 may be approximately:

${{{\Delta\theta} \propto \frac{\sin\; 60^{\circ}}{d \times \cos\; 60^{\circ}}} = \frac{{1.7}3}{d}}.$Thus, to achieve an angular resolution about 2 arcminutes, the thicknessd of transmission VBG 1850 may be at least about 1.5 mm, which is aboutthree times of the thickness of a reflection VBG having the same angularresolution, and may be difficult to achieve or may cause significantdisplay haze.

In order to reduce the physical size of a VBG-based waveguide display,reduce the thickness of the VBGs and display haze, and achieve thedesired resolution, dispersion compensation may be desired in theVBG-based waveguide display. According to certain embodiments, one ormore pairs of gratings (e.g., transmission grating) having matchinggrating vectors and operating in opposite diffraction conditions (e.g.,+1 order diffraction versus −1 order diffraction) may be used tocompensate for the dispersion caused by each other.

FIG. 19A is a front view of an example of a volume Bragg grating-basedwaveguide display 1900 with exit pupil expansion and dispersionreduction according to certain embodiments. FIG. 19B is a side view ofthe example of volume Bragg grating-based waveguide display 1900 withexit pupil expansion and dispersion reduction according to certainembodiments. Waveguide display 1900 may be similar to waveguide display1300, but may include an input coupler that is different from inputcoupler 1320. Waveguide display 1900 may include a substrate 1910, and afirst grating 1930 and a second grating 1940 formed on or in substrate1910. The input coupler may include projector optics 1920 (e.g., a lens)and an input grating 1922, rather than a prism. Display light may becollimated by projector optics 1920 and projected onto input grating1922, which may couple the display light into substrate 1910 bydiffraction as described above with respect to, for example, FIGS. 5 and6. The display light may reach a first portion 1932 of first grating1930 and may be diffracted by first portion 1932 of first grating 1930to change the propagation direction and reach other portions of firstgrating 1930, which may each diffract the display light towards secondgrating 1940. Second grating 1940 may diffract the display light out ofsubstrate 1910 at different locations to form multiple exit pupils asdescribed above.

First portion 1932 and each of other portions of first grating 1930 mayhave matching grating vectors (e.g., having a same grating vector in thex-y plane and a same grating vector and/or opposite grating vectors inthe z direction, but recorded in different exposure durations to achievedifferent diffraction efficiencies). Therefore, they may compensate forthe dispersion of display light caused by each other to reduce theoverall dispersion in one direction, due to the opposite Braggconditions (e.g., +1 order and −1 order diffractions) of thediffractions at first portion 1932 and each of other portions of firstgrating 1930. In addition, input grating 1922 and second grating 1940may have matching grating vectors (e.g., having the same grating vectorin the x-y plane and having the same and/or opposite grating vectors inthe z direction, but recorded in different exposure durations to achievedifferent diffraction efficiencies), where input grating 1922 may couplethe display light into substrate 1910, while second grating 1940 maycouple the display light out of the waveguide. Therefore, input grating1922 and second grating 1940 may compensate for the dispersion of thedisplay light caused by each other to reduce the overall dispersion inat least one direction, due to the opposite diffraction directions andopposite Bragg conditions (e.g., +1 order and −1 order diffractions) ofthe diffractions at input grating 1922 and second grating 1940. In thisway, the overall dispersion by first portion 1932 and each of otherportions of first grating 1930 may be reduced or canceled out, and theoverall dispersion by input grating 1922 and second grating 1940 mayalso be reduced or canceled out. Therefore, the overall dispersion ofthe display light by waveguide display 1900 can be minimized in anydirection. As such, a higher resolution of the displayed image may beachieved. Thus, thin reflection or transmission VBGs may be used as theinput and output couplers and may still achieve the desired resolution.Transmission VBGs may also allow the first and second gratings to be atleast partially overlapped to reduce the physical dimensions of thewaveguide display as described above.

Waveguide display 1900 may include multiple polymer layers on one ormore waveguide plates, where input grating 1922, first grating 1930, andsecond grating 1940 may each be split into multiple gratings recorded inthe multiple polymer layers. The gratings on each polymer layer maycover different respective FOVs and light spectra, and the combinationof the multiple polymer layers may provide the full FOV and spectralcoverage. In this way, each polymer layer can be thin (e.g., about 20 μmto about 100 μm) and can be exposed for fewer times (e.g., less thanabout 100) to record fewer gratings to reduce haziness, and the overallefficiency of the multiple polymer layers can still be high for the fullFOV and spectrum. In the example shown in FIGS. 19A and 19B, waveguidedisplay 1900 may include a first polymer layer 1912 and a second polymerlayer 1914 on one or more plates or substrates. Each polymer layer 1912or 1914 may include part of input grating 1922, first grating 1930,and/or second grating 1940.

FIG. 20A illustrates another example of a volume Bragg grating-basedwaveguide display 2000 with exit pupil expansion, dispersion reduction,form-factor reduction, and efficiency improvement according to certainembodiments. As waveguide display 2000, waveguide display 2000 mayinclude a substrate 2010, which may be similar to substrate 1910.Substrate 2010 may include a first surface 2012 and a second surface2014. Display light from a light source (e.g., LEDs) may be coupled intosubstrate 2010 by an input coupler 2020, and may be reflected by firstsurface 2012 and second surface 2014 through total internal reflection,such that the display light may propagate within substrate 2010 (e.g.,in −y direction). As described above, input coupler 2020 may include adiffractive coupler, such as a multiplexed VBG, which may couple displaylight of different colors into substrate 2010 at different diffractionangles.

Waveguide display 2000 may include a first grating 2030 and a secondgrating 2040 formed on first surface 2012 and/or second surface 2014.Waveguide display 2000 may also include a third grating 2060 and afourth grating 2070 formed on first surface 2012 and/or second surface2014. Third grating 2060 and fourth grating 2070 may each be amultiplexed VBG that includes multiple VBGs. In some embodiments, thirdgrating 2060, fourth grating 2070, and first grating 2030 may be on asame surface or different surfaces of substrate 2010. In someembodiments, third grating 2060, fourth grating 2070, and first grating2030 may be in different regions of a same grating or a same gratingmaterial layer.

In some embodiments, first grating 2030, third grating 2060, and fourthgrating 2070 may each include multiple VBGs. Third grating 2060 andfirst grating 2030 may be recorded in multiple exposures and undersimilar recording conditions (but may be recorded for different exposuredurations to achieve different diffraction efficiencies), such that eachVBG in third grating 2060 may match a respective VBG in first grating2030 (e.g., having the same grating vector in the x-y plane and havingthe same and/or opposite grating vectors in the z direction). Forexample, in some embodiments, a VBG in third grating 2060 and acorresponding VBG in first grating 2030 may have the same grating periodand the same grating slant angle (and thus the same grating vector), andthe same thickness. Fourth grating 2070 and first grating 2030 may alsobe recorded in multiple exposures and under similar recording conditions(but for different exposure durations), such that each VBG in fourthgrating 2070 may match a respective VBG in first grating 2030 (e.g.,having the same grating vector in the x-y plane and having the sameand/or opposite grating vectors in the z direction). In someembodiments, the recording conditions for recording third grating 2060may be different from the recording conditions for recording fourthgrating 2070, such that third grating 2060 and fourth grating 2070 mayhave different Bragg conditions (and different grating vectors) and thusmay diffract light from different FOV ranges and/or wavelength ranges toimprove the overall diffraction efficiency for visible light in a largeFOV range. In some embodiments, third grating 2060 and fourth grating2070 may have similar grating vectors and thus may diffract light fromthe same FOV ranges and/or wavelength ranges with similar or differentdiffraction efficiencies to improve the overall diffraction efficiencyfor light in certain FOV ranges and/or wavelength ranges.

In some embodiments, VBGs in first grating 2030 that match the VBGs inthird grating 2060 may be recorded in one area (e.g., an upper region)of first grating 2030, while the other VBGs in first grating 2030 thatmatch the VBGs in fourth grating 2070 may be recorded in a differentarea (e.g., a lower region) of first grating 2030. In one example, thirdgrating 2060 and fourth grating 2070 may each have a thickness about 20μm and may each include about 20 VBGs recorded through about 20exposures. In the example, first grating 2030 may have a thickness about20 μm or higher and may include about 40 VBGs recorded at differentregions through about 40 exposures. Second grating 2040 may have athickness about 20 μm or higher, and may include about 50 VBGs recordedthrough about 50 exposures.

Input coupler 2020 may couple the display light from a light source intosubstrate 2010. The display light may reach third grating 2060 directlyor may be reflected by first surface 2012 and/or second surface 2014 tothird grating 2060, where the size of the display light beam may beslightly larger than that at input coupler 2020. Each VBG in thirdgrating 2060 may diffract a portion of the display light within a FOVrange and a wavelength range that approximately satisfies the Braggcondition of the VBG to an upper region of first grating 2030. Asdescribed above, the upper region of first grating 2030 may include VBGsthat match the VBGs in third grating 2060. Therefore, while the displaylight diffracted by a VBG in third grating 2060 propagates withinsubstrate 2010 (e.g., along a direction shown by a line 2032) throughtotal internal reflection, a portion of the display light may bediffracted by the corresponding VBG in first grating 2030 to secondgrating 2040 each time the display light propagating within substrate2010 reaches first grating 2030.

Display light that is not diffracted by third grating 2060 (e.g., due toa less than 100% diffraction efficiency or due to a small FOV rangeand/or wavelength range near the Bragg condition) may continue topropagate within substrate 2010, and may reach fourth grating 2070. EachVBG in fourth grating 2070 may diffract a portion of the display lightwithin a FOV range and a wavelength range that approximately satisfiesthe Bragg condition of the VBG to a lower region of first grating 2030.As described above, the lower region of first grating 2030 may includeVBGs that match the VBGS in fourth grating 2070. Therefore, while thedisplay light diffracted by a VBG in fourth grating 2070 propagateswithin substrate 2010 (e.g., along a direction shown by a line 2034)through total internal reflection, a portion of the display light may bediffracted by the corresponding VBG in first grating 2030 to secondgrating 2040 each time the display light propagating within substrate2010 reaches first grating 2030. Second grating 2040 may expand thedisplay light from first grating 2030 in a different direction (e.g., inapproximately the y direction) by diffracting a portion of the displaylight to an eyebox 2050 (e.g., at a distance about 18 mm from secondgrating 2040 in +z or −z direction) each time the display lightpropagating within substrate 2010 reaches second grating 2040. In thisway, the display light may be expanded in two dimensions to fill eyebox2050.

FIG. 20B illustrates examples of replicated exit pupils at an eyebox2080 (e.g., eyebox 2050) of volume Bragg grating-based waveguide display2000. The exit pupils may include a first set of exit pupils 2082replicated by gratings 2060, 2030, and 2040, and a second set of exitpupils 2084 replicated by gratings 2070, 2030, and 2040. In embodimentswhere gratings 2060 and 2070 have different grating vectors, the firstset of exit pupils 2082 and the second set of exit pupils 2084 maycorrespond to different FOV ranges and/or different wavelength ranges.In embodiments where gratings 2060 and 2070 have similar gratingvectors, the first set of exit pupils 2082 and the second set of exitpupils 2084 may correspond to a same FOV range and/or wavelength range.The first set of exit pupils 2082 and the second set of exit pupils 2084may overlap or partially overlap. Thus, the pupil replication densitymay be increased, and the light may be more uniform in the eyebox, dueto the diffraction of display light by two spatially multiplexed sets ofVBGs.

In addition, the dispersion may be reduced in the two dimensions due tothe dual diffraction in each dimension by a pair of matching gratingsthat operate under opposite Bragg conditions as described above.Furthermore, display light in a broader bandwidth may be diffracted at ahigher diffraction efficiency by the gratings to the eyebox because ofthe lower number of exposures (and thus a higher refractive indexmodulation do for each VBG). Thus, the power efficiency of the waveguidedisplay may be improved. In some embodiments, first grating 2030 andsecond grating 2040 may at least partially overlap to reduce the formfactor of waveguide display 2000 as described above.

FIG. 21A illustrates another example of a volume Bragg grating-basedwaveguide display 2100 with exit pupil expansion, dispersion reduction,and form-factor reduction according to certain embodiments. As waveguidedisplay 2100, waveguide display 2100 may include a substrate 2110, whichmay be similar to substrate 2110. Substrate 2110 may include a firstsurface 2112 and a second surface 2114. Display light from a lightsource (e.g., LEDs) may be coupled into substrate 2110 by an inputcoupler 2120, and may be reflected by first surface 2112 and secondsurface 2114 through total internal reflection, such that the displaylight may propagate within substrate 2110. As described above, inputcoupler 2120 may include a diffractive coupler, such as a VBG. Waveguidedisplay 2100 may also include a first grating 2130 and a second grating2140 formed on first surface 2112 and/or second surface 2114. In theexample shown in FIG. 21A, first grating 2130 and second grating 2140may be at different locations in the x direction, and may overlap in atleast a portion of the see-through region of waveguide display 2100.First grating 2130 and second grating 2140 may be used for dual-axispupil expansion to expand the incident display light beam in twodimensions to fill an eyebox 2150 (e.g., at a distance about 18 mm fromsecond grating 2140 in +z or −z direction) with the display light. Forexample, first grating 2130 may expand the display light beam inapproximately the y direction, while second grating 2140 may expand thedisplay light beam in approximately the x direction.

In addition, waveguide display 2100 may include a third grating 2160formed on first surface 2112 and/or second surface 2114. In someembodiments, third grating 2160 and first grating 2130 may be arrangedat different locations in the y direction on a same surface of substrate2110. In some embodiments, third grating 2160 and first grating 2130 maybe in different regions of a same grating or a same grating materiallayer. In some embodiments, third grating 2160 may be spatially separatefrom first grating 2130. In some embodiments, third grating 2160 andfirst grating 2130 may be recorded in a same number of exposures andunder similar recording conditions (but may be recorded for differentexposure durations to achieve different diffraction efficiencies), suchthat each VBG in third grating 2160 may match a respective VBG in firstgrating 2130 (e.g., having the same grating vector in the x-y plane andhaving the same and/or opposite grating vectors in the z direction).

Input coupler 2120 may couple the display light from the light sourceinto substrate 2110. The display light may propagate approximately alongthe x direction within substrate 2110, and may reach third grating 2160directly or may be reflected by first surface 2112 and/or second surface2114 to third grating 2160. Each VBG in third grating 2160 may diffracta portion of the display light within a FOV range and a wavelength rangethat approximately satisfies the Bragg condition of the VBG downward tofirst grating 2130. While the display light diffracted by a VBG in thirdgrating 2160 propagates within substrate 2110 along a direction (e.g.,approximately in the y direction shown by a line 2132) through totalinternal reflection, a portion of the display light may be diffracted bythe corresponding VBG in first grating 2130 to second grating 2140 eachtime the display light propagating within substrate 2110 reaches firstgrating 2130. Second grating 2140 may then expand the display light fromfirst grating 2130 in a different direction (e.g., approximately in thex direction) by diffracting a portion of the display light to eyebox2150 each time the display light propagating within substrate 2110reaches second grating 2140. Input coupler 2120 and second grating 2140may include matching VBGs (e.g., VBGs with same grating vectors in thex-y plane and the same or opposite grating vectors in the z direction)to reduce the overall dispersion caused by input coupler 2120 and secondgrating 2140. Similarly, gratings 2130 and 2160 may include matchingVBGs (e.g., VBGs with same grating vectors in the x-y plane and havingthe same and/or opposite grating vectors in the z direction) to reducethe overall dispersion caused by gratings 2130 and 2160. Thus, theoverall dispersion by the gratings in waveguide display 2100 may bereduced or minimized.

Each of first grating 2130 and second grating 2140 may have a thicknessless than, for example, 100 μm (e.g., 20 μm), and may include, forexample, fewer than 50 VBGs. Thus, any area in the optical see-throughregion of waveguide display 2100 may include fewer than 100 VBGs. Assuch, the display haze may not be significant. In addition, firstgrating 2130 and second grating 2140 may at least partially overlap toreduce the form factor of waveguide display 2100, and thus the physicaldimensions of waveguide display 2100 may be similar to the physicaldimensions of a lens in a regular pair of eye glasses.

FIG. 21B illustrates an example of a volume Bragg grating-basedwaveguide display 2105 with exit pupil expansion, dispersion reduction,form-factor reduction, and efficiency improvement according to certainembodiments. As waveguide display 2100, waveguide display 2105 mayinclude a first grating 2135, second grating 2145, a third grating 2165,and a fourth grating 2175 formed on a first surface 2116 and/or a secondsurface 2118 of a substrate 2115. First grating 2135, a second grating2145, third grating 2165, and fourth grating 2175 may each include amultiplexed VBG that includes multiple VBGs. In some embodiments, thirdgrating 2165, fourth grating 2175, and first grating 2135 may be on asame surface of substrate 2115. In some embodiments, third grating 2165,fourth grating 2175, and first grating 2135 may be in different regionsof a same grating or a same grating material layer.

Each VBG in third grating 2165 may have a grating vector matching agrating vector of a respective VBG in first grating 2135 (e.g., havingthe same grating vector in the x-y plane and having the same and/oropposite grating vectors in the z direction). Each VBG in fourth grating2175 may have a grating vector matching a grating vector of a respectiveVBG in first grating 2135 (e.g., having the same grating vector in thex-y plane and having the same and/or opposite grating vectors in the zdirection). In some embodiments, third grating 2165 and fourth grating2175 may have different grating vectors and thus may diffract light fromdifferent FOV ranges and/or wavelength ranges to improve the overalldiffraction efficiency for visible light in a large FOV range. In someembodiments, third grating 2165 and fourth grating 2175 may have similargrating vectors and thus may diffract light from the same FOV rangesand/or wavelength ranges with similar or different diffractionefficiencies to improve the overall diffraction efficiency for light incertain FOV ranges and/or wavelength ranges.

Input coupler 2125 may couple the display light from the light sourceinto substrate 2115. The display light may reach third grating 2165directly or may be reflected by first surface 2116 and/or second surface2118 to third grating 2165. Each VBG in third grating 2165 may diffracta portion of the display light within a FOV range and a wavelength rangethat approximately satisfies the Bragg condition of the VBG to a leftregion of first grating 2135. While the display light diffracted by aVBG in third grating 2165 propagates within substrate 2115 (e.g., alonga direction shown by a line 2136) through total internal reflection, aportion of the display light may be diffracted by the corresponding VBGin first grating 2135 to second grating 2145 each time the display lightpropagating within substrate 2115 reaches first grating 2135.

Display light that is not diffracted by third grating 2165 (e.g., due toa less than 100% diffraction efficiency or due to a small FOV rangeand/or wavelength range near the Bragg condition) may continue topropagate within substrate 2115, and may reach fourth grating 2175. EachVBG in fourth grating 2175 may diffract a portion of the display lightwithin a FOV range and a wavelength range that approximately satisfiesthe Bragg condition of the VBG to a right region of first grating 2135.While the display light diffracted by a VBG in fourth grating 2175propagates within substrate 2115 (e.g., along a direction shown by aline 2138) through total internal reflection, a portion of the displaylight may be diffracted by the corresponding VBG in first grating 2135to second grating 2145 each time the display light propagating withinsubstrate 2115 reaches first grating 2135.

Second grating 2145 may expand the display light from first grating 2135in a different direction (e.g., in approximately the x direction) bydiffracting a portion of the display light to an eyebox 2155 (e.g., at adistance about 18 mm from second grating 2145 in +z or −z direction)each time the display light propagating within substrate 2115 reachessecond grating 2145. In this way, the display light may be expanded intwo dimensions to fill eyebox 2155. The resultant exit pupils mayinclude a first set of exit pupils replicated by gratings 2165, 2135,and 2145, and a second set of exit pupils replicated by gratings 2175,2135, and 2145. In embodiments where gratings 2165 and 2175 havedifferent grating vectors, the first set of exit pupils and the secondset of exit pupils may correspond to different FOV ranges and/ordifferent wavelength ranges. In embodiments where gratings 2165 and 2175have similar grating vectors, the first set of exit pupils and thesecond set of exit pupils may correspond to a same FOV range and/orwavelength range. The first set of exit pupils and the second set ofexit pupils may overlap or partially overlap. Thus, the pupilreplication density may be increased, and the light may be more uniformin the eyebox, due to the diffraction of display light by two spatiallymultiplexed sets of VBGs.

In some embodiments, the full FOV range of a display image may bedivided into two or more FOV ranges to be covered by two or more sets ofgratings. The two or more FOV ranges may be stitched together to providethe full field of view. For each FOV range, a set of gratings may beused to expand the exit pupil in two dimensions to fill an eye-box.

FIG. 22A is a front view of an example of a volume Bragg grating-basedwaveguide display 2200 including two image projectors 2220 and 2250according to certain embodiments. FIG. 22B is a side view of the exampleof volume Bragg grating-based waveguide display 2200 including two imageprojectors 2220 and 2250 according to certain embodiments. Imageprojector 2220, a first input grating 2222, a first top grating 2230,and a bottom grating 2240 may be used to provide a first portion (e.g.,the left half) of the full FOV of waveguide display 2200. Display lightfor the first portion of the full FOV may be collimated and projectedonto a first input grating 2222, which may couple the display light intoa waveguide 2210 by diffraction as described above with respect to, forexample, FIGS. 5-6. The display light may reach a first portion 2232 offirst top grating 2230 and may be diffracted by first portion 2232 offirst top grating 2230 to change the propagation direction and reachother portions of first top grating 2230, which may each diffract thedisplay light towards bottom grating 2240. Bottom grating 2240 maydiffract the display light out of waveguide 2210 at different locationsto form multiple exit pupils as described above. First portion 2232 offirst top grating 2230 and each of other portions of first top grating2230 may have similar grating parameters (but may be recorded indifferent exposure durations to achieve different diffractionefficiencies). Therefore, they may compensate the dispersion of displaylight caused by each other to reduce the overall dispersion, due to theopposite Bragg conditions (e.g., +1 order and −1 order diffractions) forthe diffractions at first portion 2232 of first top grating 2230 andeach of other portions of first top grating 2230.

In addition, first input grating 2222 and bottom grating 2240 may havesimilar grating parameters or similar grating vectors at least in thex-y plane (but may be recorded in different exposure durations toachieve different diffraction efficiencies), where first input grating2222 may couple the display light into waveguide 2210, while bottomgrating 2240 may couple the display light out of waveguide 2210.Therefore, first input grating 2222 and bottom grating 2240 maycompensate the dispersion of display light caused by each other toreduce the overall dispersion, due to the opposite diffractiondirections and opposite Bragg conditions (e.g., +1 order and −1 orderdiffractions) for the respective diffractions. In this way, thedispersion by first portion 2232 of first top grating 2230 and each ofother portions of first top grating 2230 may be canceled out, and thedispersion by first input grating 2222 and bottom grating 2240 may alsobe canceled out.

Similarly, image projector 2250, a second input grating 2252, a secondtop grating 2260, and bottom grating 2240 (or a different bottomgrating) may be used to provide another portion (e.g., the right half)of the full FOV of waveguide display 2200. As described above, bottomgrating 2240 may be used for both portions of the field of view, or mayinclude two gratings each for a portion of the field of view. Thedispersion by a first portion 2262 and each of other portions of secondtop grating 2260 may be canceled out, and the dispersion by second inputgrating 2252 and bottom grating 2240 may also be canceled out.Therefore, the overall dispersion of the display light by waveguidedisplay 2200 can be minimized in any direction. As such, a higherresolution of the displayed image may be achieved even if the polymerlayers are thin and transmission VBGs are recorded in the thin polymerlayers.

Waveguide display 2200 may include multiple polymer layers on one ormore waveguide plates, such as a first waveguide plate 2212 and a secondwaveguide plate 2214. Input gratings 2222 and 2252, top gratings 2230and 2260, and bottom grating 2240 may each be split into multiplegratings recorded in the multiple polymer layers. The gratings on eachpolymer layer may cover different respective FOVs and light spectra. Thecombination of the multiple polymer layers may provide the full FOV andspectral coverage. In this way, each polymer layer can be thin (e.g.,about 20 μm to about 100 μm) and can be exposed for fewer times (e.g.,less than about 100) to record fewer gratings, thus reducing hazinessfor see-through images. The overall efficiency of the multiple polymerlayers can still be high for the full FOV and visible light spectrum.

FIG. 23A is a front view of an example of a volume Bragg grating-basedwaveguide display 2300 including a single image projector 2320 andgratings for field-of-view stitching according to certain embodiments.FIG. 23B is a side view of the example of volume Bragg grating-basedwaveguide display 2300 with image projector 2320 and the gratings forfield-of-view stitching according to certain embodiments. Waveguidedisplay 2300 may include multiple polymer layers on one or morewaveguide plates 2310. Image projector 2320, an input grating 2330, atop grating 2340, and a bottom grating 2350 may be used to provide afirst portion (e.g., the left half) of the full FOV of waveguide display2300. As described above, display light for the first portion of the FOVmay be collimated and projected onto input grating 2330, which maycouple the display light into a waveguide plate 2310 by diffraction asdescribed above. The display light may reach a first portion of topgrating 2340 and may be diffracted by the first portion of top grating2340 to other portions of top grating 2340, which may each diffract thedisplay light towards bottom grating 2350. Bottom grating 2350 maydiffract the display light out of waveguide plate 2310 at differentlocations to replicate exit pupils as described above. The first portionand each of the other portions of top grating 2340 may compensate forthe dispersion caused by each other, and input grating 2330 and bottomgrating 2350 may also compensate for the dispersion caused by each otheras described above.

Image projector 2320, an input grating 2332, a top grating 2342, and abottom grating 2352 may be used to provide a portion (e.g., the righthalf) of the full FOV of waveguide display 2300. The display light maybe collimated and coupled into waveguide plate 2310 by input grating2332. The display light may reach a first portion of top grating 2342and may be diffracted by the first portion of top grating 2342 to otherportions of top grating 2342, which may each diffract the display lighttowards bottom grating 2352. Bottom grating 2352 may diffract thedisplay light out of waveguide plate 2310 at different locations toreplicate exit pupils as described above. The first portion and each ofother portions of top grating 2342 may compensate for the dispersioncaused by each other, and input grating 2332 and bottom grating 2352 mayalso compensate for the dispersion caused by each other as describedabove.

Waveguide display 2300 may include multiple polymer layers on one ormore waveguide plates 2310, where input gratings 2330 and 2332, topgratings 2340 and 2342, and bottom gratings 2350 and 2352 may each besplit into multiple gratings recorded in the multiple polymer layers,where the gratings on each polymer layer may cover different respectiveFOVs and light spectra. The combination of the multiple polymer layersmay provide the full FOV and spectral coverage. In this way, eachpolymer layer can be thin (e.g., about 20 μm to about 100 μm) and can beexposed for fewer times (e.g., less than about 100) to record fewergratings to reduce haziness, and the overall efficiency of the multiplepolymer layers can still be high for the full FOV and the visible lightspectrum.

In the example shown in FIG. 23B, each of input grating 2330, topgrating 2340, and bottom grating 2350 may be split into two multiplexedgratings that are each recorded in a respective polymer layer and eachcover a respective FOV, where multiple VBGs may be recorded in eachrespective polymer layer to form a multiplexed grating. Similarly, eachof input grating 2332, top grating 2342, and bottom grating 2352 may besplit into two multiplexed gratings that are each recorded in arespective polymer layer and each cover a respective FOV, where multipleVBGs may be recorded in each respective polymer layer to form amultiplexed grating. As shown in FIG. 23B, input gratings 2332 and 2330may be in different polymer layers. Similarly, top gratings 2340 and2342 may be in different polymer layers, and bottom gratings 2350 and2352 may be in different polymer layers. Thus, the crosstalk betweenthem can be reduced.

FIG. 24 illustrates an example of a volume Bragg grating-based waveguidedisplay 2400 including multiple grating layers for different fields ofview and/or light wavelengths according to certain embodiments.VBG-based waveguide display 2400 may be an example of VBG-basedwaveguide display 2300 described above. In waveguide display 2400,gratings may be spatially multiplexed along the z direction. Forexample, waveguide display 2400 may include multiple substrates, such assubstrates 2410, 2412, 2414, and the like. The substrates may include asame material or materials having similar refractive indexes. One ormore VBGs (e.g., VBGs 2420, 2422, 2424, etc.) may be made on eachsubstrate, such as recorded in a holographic material layer formed onthe substrate. The VBGs may be reflection gratings or transmissiongratings. The substrates with the VBGs may be arranged in a substratestack along the z direction for spatial multiplexing. Each VBG may be amultiplexed VBG that includes multiple gratings designed for differentBragg conditions to couple display light in different wavelength rangesand/or different FOVs into or out of the waveguide.

In the example shown in FIG. 24, VBG 2420 may couple light 2434 from apositive field of view into the waveguide as shown by a light ray 2444within the waveguide. VBG 2422 may couple light 2430 from around 0°field of view into the waveguide as shown by a light ray 2440 within thewaveguide. VBG 2424 may couple light 2432 from a negative field of viewinto the waveguide as shown by a light ray 2442 within the waveguide. Asdescribed above, each of VBGs 2420, 2422, and 2424 may be a multiplexedVBG with many exposures, and thus may couple light from different FOVranges into or out of the waveguide.

FIG. 25 illustrates the fields of view of multiple gratings in anexample of a volume Bragg grating-based waveguide display according tocertain embodiments. In some embodiments, each of the gratings may be ina respective grating layer or on a respective waveguide plate. Each ofthe gratings may be a multiplexed grating including many exposures, andmay be used to couple display light from multiple FOV ranges into or outof the waveguide at high efficiencies. For example, a curve 2510 mayshow the diffraction efficiency of a first VBG (e.g., VBG 2422 of FIG.24) for light from different fields of view. A curve 2520 may show thediffraction efficiency of a second VBG (e.g., VBG 2420 of FIG. 24) forlight from different fields of view. A curve 2530 may show thediffraction efficiency of a third VBG (e.g., VBG 2424 of FIG. 24) forlight from different fields of view. The first, second, and third VBGs,when arranged in a stack, may more uniformly diffract light in the fullfield of view (e.g., from about −20° to about 20°) at high efficiencies.In some embodiments, the first VBG, the second VBG, and the third VBGmay be used to couple display light of the same color. Different sets ofVBGS may be used to cover the full field of view for display light ofdifferent colors.

A VBG designed to diffract light in one wavelength and from one angularrange may also diffract light in another wavelength and from anotherangular range. For example, a VBG characterized by a particular periodand slant angle may diffract light in different wavelengths and fromdifferent incident angles.

FIG. 26A illustrates the diffraction of light of different colors fromcorresponding fields of view by an example of a volume Bragg grating2610 and. As shown in the example, VBG 2610 may diffract blue light 2602from a first incident angle into a waveguide at a first diffractionangle. VBG 2610 may also diffract green light 2604 from a secondincident angle into the waveguide at a second diffraction angle. VBG2610 may further diffract red light 2606 from a third incident angleinto the waveguide at a third diffraction angle.

FIG. 26B illustrates the relationship between grating periods of volumeBragg gratings and the corresponding fields of view for incident lightof different colors. A curve 2620 shows that red light from differentfields of view may be diffracted by VBGs having different gratingperiods. Similarly, a curve 2630 shows that green light from differentfields of view may be diffracted by VBGs having different gratingperiods, and a curve 2630 shows that blue light from different fields ofview may be diffracted by VBGs having different grating period. FIG. 26Balso shows that a VBG having a particular grating period and slant anglemay diffract light in different wavelengths and from different incidentangles (e.g., from different fields of view). A region 2605 in FIG. 26Bshows gratings that may diffract light of two or more colors from two ormore respective FOVs. For example, a dashed line 2650 in FIG. 26B maycorrespond to a VBG with a grating period about 450 nm, where the VBGmay diffract red light from about −7° field of view, diffract greenlight from about 2° field of view, and diffract blue light from about 6°field of view.

As described above, VBGs may be reflection VBGs or transmission VBGs.Reflection VBGs and transmission VBGs can have different diffractionproperties. For example, as described above with respect to FIGS. 18Aand 18B, reflection gratings may have relatively lower dispersion thantransmission gratings of similar thicknesses. Transmission gratings usedas output gratings may allow for the overlapping of the gratings fortwo-dimensional exit pupil replication to reduce the physical size ofthe waveguide display as described above with respect to FIG. 16, whilereflection gratings may not as described above with respect to FIG. 15.

FIG. 27A illustrates the diffraction efficiencies of examples oftransmission volume Bragg gratings with the same thickness but differentrefractive index modulations. The diffraction efficiencies may bepolarization-dependent. A curve 2710 shows the diffraction efficienciesof the examples of transmission VBGs for s-polarized light, while acurve 2720 shows the diffraction efficiencies of the examples oftransmission VBGs for p-polarized light. A curve 2730 shows the averagediffraction efficiencies of the examples of transmission VBGs for s- andp-polarized light (e.g., unpolarized light). As shown in FIG. 27A, curve2710 and curve 2720 may correspond to functions proportional to a squareof a sinusoidal function (e.g., ∝ sin²(a×n₁×D)). The diffractionefficiencies of transmission gratings may increase or decrease with theincrease of the refractive index modulation. Thus, increasing therefractive index modulation of a transmission VBG may not necessarilyincrease the diffraction efficiency of the transmission VBG.

FIG. 27B illustrates the diffraction efficiencies of examples ofreflection volume Bragg gratings with the same thickness but differentrefractive index modulations. The diffraction efficiencies forreflection VBGs are also polarization-dependent. A curve 2760 shows thediffraction efficiencies of the examples of reflection VBGs fors-polarized light, while a curve 2720 shows the diffraction efficienciesof the examples of reflection VBGs for p-polarized light. A curve 2730shows the average diffraction efficiencies of the examples of reflectionVBGs for s- and p-polarized light (e.g., unpolarized light). As shown inFIG. 27B, the diffraction efficiencies of reflection VBGs may increasewith the increase of the refractive index modulation (e.g., ∝tanh²(a×n₁×D)) and may saturate when the refractive index modulationreaches a certain value.

FIGS. 28A-28D illustrate the diffraction efficiency of examples oftransmission volume Bragg gratings with different refractive indexmodulations as a function of the deviation of the incident angle fromthe Bragg condition. A curve 2810 in FIG. 28A shows the diffractionefficiency of an example of a transmission VBG with a refractive indexmodulation about 0.002, where the peak diffraction efficiency of themain lobe is close to 100%. A curve 2820 in FIG. 28B shows thediffraction efficiency of an example of a transmission VBG with arefractive index modulation about 0.004, where the peak diffractionefficiency drops to about 0 at about 0°, the diffraction efficiencycurve 2820 has two peaks, and the sidelobes increase, compared with thetransmission VBG of FIG. 28A. A curve 2830 in FIG. 28C shows thediffraction efficiency of an example of a transmission VBG with arefractive index modulation about 0.0054, where the peak diffractionefficiency, the FWHM angular range of the main lobe, and the sidelobesmay increase compared with the transmission VBG of FIG. 28B. A curve2840 in FIG. 28D shows the diffraction efficiency of an example of atransmission VBG with a refractive index modulation about 0.0078, wherethe peak diffraction efficiency decreases, the diffraction efficiencycurve 2840 has two peaks, and the sidelobes increase, compared with thetransmission VBG of FIG. 28C.

FIGS. 29A-29D illustrate the diffraction efficiency of examples ofreflection volume Bragg gratings having different refractive indexmodulations as a function of the deviation of the incident angle fromthe Bragg condition. A curve 2910 in FIG. 29A shows the diffractionefficiency of an example of a reflection VBG with a refractive indexmodulation about 0.002, where the peak diffraction efficiency of themain lobe is greater than 80%. A curve 2920 in FIG. 29B shows thediffraction efficiency of an example of a reflection VBG with arefractive index modulation about 0.004, where the peak diffractionefficiency increases to 100%, the FWHM angular range of the main lobeincreases, and the sidelobes increase compared with the reflection VBGof FIG. 29A. A curve 2930 in FIG. 29C shows the diffraction efficiencyof an example of a reflection VBG with a refractive index modulationabout 0.0054, where the peak diffraction efficiency is about 100%, theFWHM angular range of the main lobe further increases, and the sidelobesfurther increase as well compared with the reflection VBG of FIG. 29B. Acurve 2940 in FIG. 29D shows the diffraction efficiency of an example ofa reflection VBG with a refractive index modulation about 0.0078, wherethe peak diffraction efficiency is about 100%, the FWHM angular range ofthe main lobe further increases, and the sidelobes further increase aswell compared with the reflection VBG of FIG. 29C.

For transmission VBGs, the diffraction efficiency of a polarized lightmay be a function of the refractive index modulation (e.g., ∝sin²(a×n₁×D)) as shown in FIG. 27A. In addition, the diffractionefficiency may be color dependent. For example, a transmission VBG mayneed a lower refractive index modulation to reach the first diffractionpeak shown in FIG. 27A for one color (e.g., blue) than for another color(e.g., green or red). A grating with a certain refractive indexmodulation less than the refractive index modulation corresponding tothe first diffraction peak shown in FIG. 27A may have a higherdiffraction efficiency for blue light than for green or red light.

FIGS. 30A-30C illustrate the diffraction efficiency of an example of atransmission VBG with a first refractive index modulation (e.g., about0.01). The transmission VBG may diffract light of different colors fromdifferent respective fields of view with different respectivediffraction efficiencies as described above with respect to FIGS. 26Aand 26B. For example, a curve 3010 in FIG. 30A may illustrate thediffraction efficiency of the transmission VBG for blue light from about14° field of view, where the peak diffraction efficiency may be close to100%. A curve 3020 in FIG. 30B may illustrate the diffraction efficiencyof the same transmission VBG for green light from about 10° field ofview, where the peak diffraction efficiency has not reached 100% yet(e.g., at about 90%). A curve 3030 in FIG. 30C may illustrate thediffraction efficiency of the same transmission VBG for red light fromabout 3° field of view, where the peak diffraction efficiency may beabout 80%.

FIGS. 30D-30F illustrate the diffraction efficiency of an example of atransmission VBG with a second refractive index modulation (e.g.,0.012). The transmission VBG may be different from the transmission VBGassociated with FIGS. 30A-30C in only the refractive index modulation.The transmission VBG may diffract light of different colors fromdifferent respective fields of view with different respectivediffraction efficiencies. For example, a curve 3012 in FIG. 30D mayillustrate the diffraction efficiency of the transmission VBG for bluelight from about 14° field of view, where the peak diffractionefficiency may have decreased from the peak value of about 100% shown inFIG. 30A because the refractive index modulation is greater than therefractive index modulation associated with the first diffractionefficiency peak as shown in FIG. 30A. A curve 3022 in FIG. 30E mayillustrate the diffraction efficiency of the same transmission VBG forgreen light from about 10° field of view, where the peak diffractionefficiency may have increased (e.g., greater than 90%). A curve 3032 inFIG. 30F may illustrate the diffraction efficiency of the sametransmission VBG for red light from about 3° field of view, where thepeak diffraction efficiency may have increased to greater than 80%.

FIGS. 30G-30I illustrate the diffraction efficiency of an example of atransmission VBG with a third refractive index modulation (e.g., 0.015).The transmission VBG may be different from the transmission VBGsassociated with FIGS. 30A-30F in only the refractive index modulation.The transmission VBG may diffract light of different colors fromdifferent respective fields of view with different respectivediffraction efficiencies. For example, a curve 3014 in FIG. 30G mayillustrate the diffraction efficiency of the transmission VBG for bluelight from about 14° field of view, where the peak diffractionefficiency may have further decreased from the value shown in FIG. 30Dbecause the refractive index modulation is greater than the refractiveindex modulation associated with the first diffraction efficiency peakas shown in FIG. 30A. A curve 3024 in FIG. 3011 may illustrate thediffraction efficiency of the same transmission VBG for green light fromabout 10° field of view, where the peak diffraction efficiency may alsohave decreased from its maximum value. A curve 3034 in FIG. 30I mayillustrate the diffraction efficiency of the same transmission VBG forred light from about 3° field of view, where the peak diffractionefficiency may have further increased.

In contrast, for reflection VBGs, as shown in FIG. 27B and FIGS.29A-29D, the diffraction efficiency may not decrease with the increaseof the refractive index modulation. The FWHM angular range of the mainlobe and the sidelobes of the diffraction efficiency curve may increasewith the increase of the refractive index modulation.

FIG. 31A illustrates the minimum refractive index modulations oftransmission volume Bragg gratings with different grating periods inorder to achieve diffraction saturation for different colors. A curve3110 shows the minimum refractive index modulations of transmission VBGsto achieve the maximum diffraction efficiency for red light, a curve3120 shows the minimum refractive index modulations of transmission VBGsto achieve the maximum diffraction efficiency for green light, while acurve 3130 shows the minimum refractive index modulations oftransmission VBGs to achieve the maximum diffraction efficiency for bluelight. As illustrated, for a grating with a given grating period andthickness, the minimum refractive index modulation to achieve themaximum diffraction efficiency may vary for different colors. Forexample, the minimum refractive index modulation for maximum diffractionefficiency for blue light may be lower than that for green light or redlight. Thus, as also illustrated in FIGS. 30A-30I, for a grating thatcan diffract light in multiple colors, when the refractive indexmodulation is at a value that can achieve the highest diffractionefficiency for blue light, the diffraction efficiencies of the samegrating for green light and red light may be lower; when the refractiveindex modulation is at a value that can achieve the highest diffractionefficiency for red light, the diffraction efficiencies of the samegrating for blue light and green light may decrease from their peakvalues. Therefore, there may need to be some tradeoff between thediffraction efficiencies for different colors.

FIG. 31B illustrates a curve 3140 that shows the refractive indexmodulations of transmission gratings having different grating periods inorder to avoid the refractive index modulation saturation for any color.For example, for gratings that may diffract blue light, the refractiveindex modulations may be determined based on the refractive indexmodulation saturation for blue light. For gratings that may onlydiffraction green and red light, the refractive index modulation may bedetermined based on the refractive index modulation saturation for greenlight. For gratings that may only diffract red light, the refractiveindex modulation may be determined based on the refractive indexmodulation saturation for red light.

As described above, in order to cover the full field of view for red,green, and blue light, a VBG may be a multiplexed grating that isexposed to different recording light patterns multiple times, where eachexposure may record a grating that may diffract red, green, and bluelight from different respective fields of view. The gratings in themultiplexed VBG may have different grating periods. The multiplexed VBGmay be used to diffract light of all colors from the full field of view.In addition, the gratings in the multiplexed VBG may have differentrefractive index modulations in order to optimize the diffractionefficiencies for different colors.

FIG. 31C is a diagram 3150 illustrating an example of a grating layerincluding multiplexed VBGs of different pitches and different refractiveindex modulations for optimized the diffraction efficiency anddiffraction efficiency uniformity according to certain embodiments. Eachdata point 3152 in diagram 3150 shows the period of a grating and thecorrespond refractive index modulation. In the illustrated example, thegrating layer may include more than 40 gratings. The grating layer mayhave a maximum refractive index modulation about 0.08. Each grating mayhave a refractive index modulation about 0.002 or lower. The multiplexedgratings may, in combination, provide the full FOV for visible light.

It may generally be desirable to multiplex more gratings in amultiplexed VBG to increase the diffraction efficiency of light for alarge field of view. However, crosstalk may occur between gratings whenmany gratings are multiplexed in a multiplexed VBG.

FIG. 32A illustrates crosstalk caused by an example of a multiplexedvolume Bragg grating in a waveguide display 3200. Waveguide display 3200may include a multiplexed input grating that includes an input grating3212. Waveguide display 3200 may also include a multiplexed outputgrating 3210 that includes two or more output gratings, such as a firstoutput grating 3214 and a second output grating 3216, that may berecorded in a same grating layer or multiple grating layers. Displaylight in a first color and for a first field of view may be coupled intoa waveguide by input grating 3212, and may be coupled by first outputgrating 3214 out of the waveguide at a desired angle, such as at anoutput angle equal to the input angle (e.g., about 90° in theillustrated example). Input grating 3212 and first output grating 3214may have matching grating vectors (e.g., in at least the x-y plane) andthus may compensate the dispersion caused by each other and keep theoutput angle equal to the input angle.

The FOV associated with second output grating 3216 may at leastpartially overlap with the first FOV associated with first outputgrating 3214 due to the non-zero width of the diffraction efficiencycurve for each grating as shown in, for example, FIGS. 28A-30I.Therefore, the display light from the first field of view and coupledinto the waveguide by input grating 3212 may be at least partiallycoupled out of the waveguide at an undesired angle by second outputgrating 3216. Because of the grating vector mismatch between inputgrating 3212 and second output grating 3216, the input angle (e.g.,about 90° in the example) and the output angle of the display light inthe first FOV and coupled out the waveguide by second output grating3216 may be different as shown in FIG. 32A. Thus, an undesired ghostimage may be generated.

FIG. 32B illustrates the relationship between grating periods of volumeBragg gratings and the corresponding fields of view for incident lightof different colors. As illustrated, a same VBG (e.g., a VBG representedby a line 3230) may diffract red light at a first wavelength from anegative field of view (as indicated by the intersection of line 3230and a curve 3240). The same VBG may also diffract red light at adifferent (e.g., second) wavelength from a different negative field ofview (as indicated by the intersection of line 3230 and a curve 3242).The red light at the first wavelength and the second wavelength may beemitted by a same light source (e.g., a red LED) that emits light in anarrow spectral range. Similarly, the same VBG may diffract green lightat a third wavelength from a positive field of view (as indicated by theintersection of line 3230 and a curve 3250) and green light at adifferent (e.g., fourth) wavelength from a different positive field ofview (as indicated by the intersection of line 3230 and a curve 3252).The green light at the third wavelength and the fourth wavelength may beemitted by a same light source (e.g., a green LED) that emits light in anarrow spectral range. The same VBG may further diffract blue light at afifth wavelength from a positive field of view (as indicated by theintersection of line 3230 and a curve 3260) and blue light at adifferent (e.g., sixth) wavelength from a different positive field ofview (as indicated by the intersection of line 3230 and a curve 3262).The blue light at the fifth wavelength and the sixth wavelength may beemitted by a same light source (e.g., a blue LED) that emits light in anarrow spectral range.

In some cases, ghost effects may be caused by undesired diffraction ofdisplay light for a first field of view by a grating for a differentfield of view. For example, ghost images may exist if the display lightfor the left half of the FOV is diffracted by the top grating for theright half of the FOV or if the display light for the right half of theFOV is diffracted by the top grating for the left half of the FOV. Insome embodiments, to reduce the ghost effects, the two or more topgratings may be offset from each other and may not overlap. In someembodiments, the two or more top gratings may be designed such that theundesired diffraction of display light by a grating may not reach theeyebox and thus may not be observed by the user.

As described above, transmission grating and reflection grating may havedifferent performance characteristics, such as diffraction efficiency,diffraction efficiency saturation, dispersion, FWHM angular range, andthe like. For example, transmission grating may have broader Bragg peaklinewidth than reflection grating. In addition, the Bragg peak linewidthfor a transmission VBG or reflection VBG may vary with the correspondingfield of view.

FIG. 33A illustrates the linewidths of the Bragg peaks of transmissionvolume Bragg gratings and reflection volume Bragg gratings for differentfields of view. A curve 3310 shows the linewidths of Bragg peaks oftransmission VBGs for different fields of the view. Curve 3310 showsthat the linewidth of the Bragg peak for a transmission VBG may increasesignificantly with the increase of the corresponding field of view. Acurve 3320 illustrates the linewidths of the Bragg peaks of reflectionVBGs for different fields of view. Curve 3320 shows that the linewidthof the Bragg peak for a reflection VBG may only increase slightly withthe increase of the corresponding field of view.

FIG. 33B illustrates examples of Bragg peaks 3330 of transmission volumeBragg gratings for different fields of view. As shown, the linewidth ofa transmission VBG for a larger field of view may be much wider than thelinewidth of a transmission VBG for a smaller field of view, and thusmay cover a larger FOV range.

FIG. 33C illustrates examples of Bragg peaks 3340 of reflection volumeBragg gratings for different fields of view. As shown, the linewidth ofa reflection VBG for a larger field of view may be approximately thesame as the linewidth of a reflection VBG for a smaller field of view.

FIG. 34A illustrates trade-off between crosstalk and efficiency in anexample of a multiplexed volume Bragg grating including multiple VBGs.In the example shown in FIG. 34A, the VBGs may be loosely multiplexed toavoid Bragg peak overlap and thus crosstalk between the VBGs for bluelight from large positive fields of view as shown by a curve 3410. Asdescribed above, the VBGs may also diffract light of other colors fromother fields of view. Thus, the gratings for diffracting blue light frompositive fields of view may also diffract red light from negative fieldsof view. However, because the gratings are loosely multiplexed and thelinewidths of Bragg peaks for transmission gratings are narrower atnegative fields of view as described above with respect to FIGS.33A-33B, red light from some negative fields of view may not bediffracted by the gratings as shown by gaps between peaks in a cure3420, thus reducing the efficiency for red light at certain negativefields of view.

FIG. 34B illustrates trade-off between crosstalk and efficiency in anexample of a multiplexed volume Bragg grating that includes multipleVBGs. In the illustrated example, the VBGs may be densely multiplexed toincrease the coverage of the negative fields of view for red light asshown by a curve 3440. The densely multiplexed VBGs may also diffractblue light from positive fields of view. Because the VBGs are denselymultiplexed and the linewidths of Bragg peaks for transmission gratingsare broader at the positive fields of view, the Bragg peaks of bluelight at positive fields of view may overlap and cause crosstalk betweenthe VBGs for blue light from large positive fields of view as shown by acurve 3430.

Thus, in transmission gratings, it can be difficult to both minimize thecrosstalk and maximize the efficiency. In many cases, the maximumachievable efficiency of transmission VBG-based waveguide display may belimited by the maximum allowable crosstalk.

FIG. 35A illustrates the relationship between the minimum diffractionefficiency and the total refractive index modulation and thecorresponding crosstalk in multiplexed transmission volume Bragggratings. The horizontal axis of FIG. 35A corresponds to the desiredminimum efficiency. Data points 3520 show the minimum refractive indexmodulations in order to achieve the corresponding desired minimumdiffraction efficiencies. Data points 3510 show the maximum crosstalkvalues associated with the corresponding minimum refractive indexmodulations in order to achieve the corresponding desired minimumefficiencies.

In the example shown in FIG. 35A, the desired crosstalk may be lessthan, for example, 0.06 (such that the checker board contrast can beabout 30) as shown by a dashed line 3530. Each waveguide plate may havetwo polymer layers attached to it. The maximum refractive indexmodulation in each polymer layer may be, for example, about 0.05 suchthat the total refractive index modulation can be about 0.1 as indicatedby the dashed line 3540. As shown by a data point 3542, when the totalrefractive index modulation of the two polymer layers is 0.1 to achievea desired efficiency, the crosstalk may be much higher than the maximumallowable crosstalk indicated by dashed line 3530. As shown by a datapoint 3532, to achieve a crosstalk less than 0.06, the maximumrefractive index modulation of the polymer layers may not be fullyutilized, and the minimum efficiency may be relatively low. In theexample shown by data point 3532 in FIG. 35A, only about 20% of thetotal refractive index modulation of the two polymer layers may beutilized in order to achieve the crosstalk performance. Thus, theefficiency of transmission VBG-based waveguide display may be limited bythe maximum allowable crosstalk.

FIG. 35B illustrates the relationship between the minimum diffractionefficiency and the total refractive index modulation and thecorresponding crosstalk in multiplexed reflection volume Bragg gratings.The horizontal axis corresponds to the desired minimum efficiency. Datapoints 3570 show the refractive index modulations in order to achievethe corresponding desired minimum efficiencies. Data points 3560 showthe maximum crosstalk values associated with the correspondingrefractive index modulations in order to achieve the correspondingdesired minimum efficiencies.

In the example shown in FIG. 35B, each waveguide plate may have twopolymer layers attached to it. The maximum refractive index modulationin each polymer layer may be, for example, about 0.05, such that thetotal refractive index modulation can be, for example, about 0.1 asindicated by the dashed line 3580. As shown by a point 3582 in FIG. 35B,when the maximum refractive index modulation of the polymer layers(e.g., 0.1) is fully utilized, the crosstalk of the grating is stillmuch lower than the maximum allowable crosstalk indicated by line 3590(e.g., about 0.06), and the efficiency may be relatively high. Thus, ina reflection VBG-based waveguide display, the diffraction efficiency maybe limited by the maximum refractive index modulation of the polymerlayer. In various embodiments, transmission gratings and reflectiongratings may be selected based on the design considerations, such as theform factor, efficiency, image quality, and the like.

Based on the characteristics of the transmission VBGs and reflectionVBGs, and the desired characteristics of a waveguide display, such asthe efficiency, field of view, resolution, contrast, crosstalk, ghostimage, rainbow effect, physical dimension, and the like, transmissionVBGs or reflection VBGs may be selected to implement the waveguidedisplay. For example, as described above with respect to FIG. 27B andFIGS. 29A-29D, for a reflection grating, the diffraction efficiency maysaturate when the refractive index modulation is above a thresholdvalue. The FWHM angular range or the FWHM wavelength range may bebroadened as the refractive index modulation continues to increase. Suchproperties of reflection VBGs may be utilized in some waveguide systems.

For example, in an example of a waveguide display, the light sources ina project may emit light with a wavelength bandwidth about 10 nm toabout 30 nm. For a unsaturated reflection VBG with a thickness about 50μm, the FWHM wavelength range may be about 1 nm. Thus, multiple VBGs maybe needed in order to diffract the emitted light in the wavelengthbandwidth of the light source. The FWHM wavelength range of a saturatedreflection VBG with a thickness about 50 μm may be much broader than 1nm, and thus fewer reflection VBGs may be needed to diffract the emittedlight in the wavelength bandwidth of the light source.

FIG. 36 illustrates an example of a waveguide display 3600 includingspatially multiplexed reflection volume Bragg gratings having differentrefractive index modulations according to certain embodiments. Thereflection VBGs shown in FIG. 36 may be used for one-dimensional pupilexpansion and dispersion compensation. It is noted that the reflectionVBGs shown in FIG. 36 are for illustration purposes only. In someembodiments, additional reflection or transmission VBG gratings 3615 maybe used to expand the pupil in another dimension to achieve twodimensional pupil expansion as described above. For example, VBGgratings 3615 may include another set of reflection VBGs that may beused for pupil expansion and dispersion compensation in a seconddimension substantially perpendicular to the first dimension asdescribed above.

In the example shown in FIG. 36, waveguide display 3600 may include afirst reflection grating 3610 and a second reflection grating 3620.First reflection grating 3610 and second reflection grating 3620 mayhave matching grating vectors, such as the same grating vector in thex-y plane and the same and/or opposite grating vectors in the zdirection. For example, first reflection grating 3610 and secondreflection grating 3620 may have some same grating parameters, such asthe grating period, slant angle, and thickness, and the like. Firstreflection grating 3610 and second reflection grating 3620 maycompensate the dispersion caused by each other as described above.

In some embodiments, first reflection grating 3610 may be an example ofthe input gratings described above, such as input gratings 1922, 2222,2252, 2330, 2332, and the like. Second reflection grating 3620 may be anexample of the output gratings or bottom gratings described above, suchas second grating 1940, bottom grating 2240, bottom gratings 2350 and2352, and the like. First reflection grating 3610 and second reflectiongrating 3620 may be used to couple display light into and out of awaveguide, respectively.

In some embodiments, first reflection grating 3610 may be an example offirst portion 1932 of first grating 1930, first portion 2232 of firsttop grating 2230, first portion 2262 of second top grating 2260, firstportion of top grating 2340, first portion of top grating 2342, and thelike. Second reflection grating 3620 may be an example of other portionsof first grating 1930, first top grating 2230, second top grating 2260,top grating 2340, top grating 2342, and the like.

In waveguide display 3600, first reflection grating 3610 and secondreflection grating 3620 may have different refractive index modulations.For example, first reflection grating 3610 may be heavily saturated, andthus the diffraction efficiency of first reflection grating 3610 may beapproximately shown by a diagram 3612, where the FWHM wavelength range(and/or the FWHM angular range) may be wide to cover a large wavelengthrange (and/or a large FOV range). Thus, first reflection grating 3610may diffract display light in a large wavelength range (and/or a largeFOV range).

Second reflection grating 3620 may include multiple sections 3622, 3624,3626, and the like. Display light diffracted by first reflection grating3610 (e.g., coupled into the waveguide or deflected to a differentdirection) may propagate with the waveguide through total internalreflection and may directly or indirectly (e.g., through gratings 3615)reach each of the multiple sections of second reflection grating 3620.The multiple sections of second reflection grating 3620 may each couplea portion of the display light, for example, out of the waveguide ortowards an output (or bottom) gratings. Each of the multiple sections3622, 3624, 3626, and the like may have a different respectiverefractive index modulation, and thus may be saturated at a differentrespective level and may have a different respective FWHM wavelengthrange (and/or FWHM angular range). For example, a first section 3622 mayhave a refractive index modulation that is below, at, or slightly abovethe saturation level, and thus may have a diffraction efficiency curveshown by a diagram 3632. A second section 3624 may have a higherrefractive index modulation and thus may have a broader FWHM wavelengthrange (and/or FWHM angular range) as shown by a diagram 3634. A thirdsection 3626 may have an even higher refractive index modulation andthus may have a much broader FWHM wavelength range (and/or FWHM angularrange) as shown by a diagram 3636. In some embodiments, secondreflection grating 3620 may include multiple (e.g., more than three)sections that may have different refractive index modulations anddifferent FWHM wavelength ranges (and/or FWHM angular ranges).

In some embodiments, first section 3622 of second reflection grating3620 may couple display light in a first wavelength (and/or FOV) rangeout of the waveguide at a high efficiency (e.g., close to 100% as shownin diagram 3632) to replicate a pupil for light in the first wavelength(and/or FOV) range. Second section 3624 of second reflection grating3620 can couple display light in a second wavelength (and/or FOV) rangeout of the waveguide at a high efficiency as shown in diagram 3634. Thesecond wavelength (and/or FOV) range may include the first wavelength(and/or FOV) range and may be wider than the first wavelength (and/orFOV) range. Because a majority or all of the light in the firstwavelength (and/or FOV range) may have been diffracted by first section3622, second section 3624 may only diffract light that is within thesecond wavelength (and/or FOV) range and has not been diffracted byfirst section 3622 as shown by areas 3644 in diagram 3634 to replicateanother pupil. Similarly, third section 3626 of second reflectiongrating 3620 can couple display light in a third wavelength (and/or FOV)range out of the waveguide at a high efficiency as shown in diagram3636. The third wavelength (and/or FOV) range may include the secondwavelength (and/or FOV) range and may be wider than the secondwavelength (and/or FOV) range. Because a majority or all of the light inthe second wavelength (and/or FOV) range may have been diffracted byfirst section 3622 and second section 3624, third section 3626 may onlydiffract light that is within the third wavelength (and/or FOV) rangeand has not been diffracted by first section 3622 and second section3624 as shown in diagram 3636 to replicate a third pupil.

In some embodiments, first reflection grating 3610 and second reflectiongrating 3620 may each be a grating in a respective multiplexed gratingthat includes multiple saturated reflection VBGs. Each saturatedreflection VBG in the multiplexed grating may diffract red, green,and/or blue light from different respective wavelength and/or FOV rangesas described above with respect to, for example, FIGS. 26A, 26B, and32B. The multiple saturated reflection VBGs may thus provide the fullFOV for red, green, and blue light of the display image emitted by thelight sources (e.g., red, green, and blue LEDs) as described above withrespect to, for example, FIGS. 19B, 22B, 23B, 25, and 33C.

In some embodiments, because the diffraction efficiency of atransmission grating may be polarization sensitive and the incomingdisplay light may be unpolarized, some components of the display lightmay not be diffracted by the grating and thus the efficiency of thewaveguide display may be reduced. To improve the efficiency forunpolarized light or light in a certain polarization state, apolarization convertor and two spatially multiplexed gratings may beused to couple the display light into or out of the waveguide.

FIG. 37 illustrates an example of a waveguide display 3700 including twomultiplexed volume Bragg gratings 3710 and 3740 and a polarizationconvertor 3730 between the two multiplexed volume Bragg gratings 3710and 3740 according to certain embodiments. In some embodiments, becausethe diffraction efficiency of a transmission grating may be polarizationsensitive and the incoming display light may be unpolarized, somecomponents of the display light may not be diffracted by the grating andthus the efficiency of the waveguide display may be reduced. To improvethe efficiency for unpolarized light or light in a certain polarizationstate, a polarization convertor and two spatially multiplexed gratingsmay be used to couple the display light into or out of the waveguide. Afirst VBG 3710 may be formed on a substrate 3720 or on a surface ofpolarization convertor 3730. A second VBG 3740 may be formed on asubstrate 3750 or on another surface of polarization convertor 3730.

Unpolarized light 3702 may include s-polarized light and p-polarizedlight. First VBG 3710 may diffract a majority of the s-polarized lightand a portion of the p-polarized light as shown by diffracted light3704. Diffracted light 3704 may be partially converted by polarizationconvertor 3730 and pass through second VBG 3740 without being diffractedby second VBG 3740 as shown by transmitted light 3706 because the Braggcondition is not satisfied. The portion 3708 of the p-polarized lightthat is not diffracted by first VBG 3710 may pass through polarizationconvertor 3730 and may be converted into s-polarized light and may bediffracted by second VBG 3740, where the diffracted light 3712 may havethe same propagation direction as transmitted light 3706. In this way,unpolarized light 3702 may be more efficiently diffracted by waveguidedisplay 3700.

External light (e.g., from an external light source, such as a lamp orthe sun) may be reflected at a surface of a grating coupler and back tothe grating coupler, where the reflected light may be diffracted by thegrating coupler to generate rainbow images. In some waveguide display,ambient light with a large incident angle outside of the see-throughfield of view of the waveguide display may also be diffracted by thegrating couplers to generate rainbow images. According to someembodiments, additional structures, such as a reflective coating layer(e.g., for light from a large see-through FOV) and/or an antireflectivecoating layer (e.g., for light from a small see-through FOV), may beused in the waveguide display to reduce optical artifacts, such asrainbow effects. For example, an angular-selective transmissive layermay be placed in front of (or behind) the waveguide and the gratingcoupler of a waveguide display to reduce the artifacts caused byexternal light source. The angular-selective transmissive layer may beconfigured to reflect, diffract, or absorb ambient light with anincident angle greater than one half of the see-through field of view ofthe waveguide display, while allowing ambient light within thesee-through field of view of the near-eye display to pass through andreach user's eyes with little or no loss. The angular-selectivetransmissive layer may include, for example, coating that may includeone or more dielectric layers, diffractive elements such as gratings(e.g., meta-gratings), nanostructures (e.g., nanowires, nano-pillars,nano-prisms, nano-pyramids), and the like.

FIG. 38 illustrates an example of a waveguide display 3800 including ananti-reflection layer 3850 and an angular-selective transmissive layer3840 according to certain embodiments. Waveguide display 3800 mayinclude a waveguide 3810 and a grating coupler 3820 at the bottomsurface of waveguide 3810. Grating coupler 3820 may be similar to thegrating couplers described above. External light 3830 incident onwaveguide 3810 may be refracted into waveguide 3810 as external light3832 and may then be diffracted by grating coupler 3820. The diffractedlight may include a 0^(th) order diffraction 3834 (e.g., refractivediffraction) and a −1st order diffraction (not shown). The height,period, and/or slant angle of grating coupler 3820 may be configuredsuch that the −1st order diffraction may be reduced or minimized for theexternal light.

Waveguide display 3800 may include anti-reflection layer 3850 on bottomsurface 3822 of grating coupler 3820. Anti-reflection layer 3850 mayinclude, for example, one or more dielectric thin film layers or otheranti-reflection layers coated on bottom surface 3822, and may be used toreduce the reflection of the external light at bottom surface 3822.Thus, little or no external light may be reflected at bottom surface3822 of grating coupler 3820 back to grating coupler 3820, and thereforethe rainbow ghost that might otherwise be formed due to the diffractionof external light reflected at bottom surface 3822 by grating coupler3820 may be reduced or minimized. Some portions of the display light maybe diffracted by grating coupler 3820 and may be coupled out ofwaveguide 3810 towards user's eyes (e.g., due to −1^(st) orderdiffraction). Anti-reflection layer 3850 may also help to reduce thereflection of the portions of the display light that are coupled out ofwaveguide 3810 by grating coupler 3820.

Angular-selective transmissive layer 3840 may be coated on the topsurface of waveguide 3810 or grating coupler 3820. Angular-selectivetransmissive layer 3840 may have a high reflectivity, high diffractionefficiency, or high absorption for incident light with an incident anglegreater than a certain threshold value, and may have a low loss forincident light with an incident angle lower than the threshold value.The threshold value may be determined based on the see-through field ofview of waveguide display 3800. For example, incident light 3860 with anincident angle greater than the see-through field of view may be mostlyreflected, diffracted, or absorbed by angular-selective transmissivelayer 3840, and thus may not reach waveguide 3810. External light 3830with an incident angle within the see-through field of view may mostlypass through angular-selective transmissive layer and waveguide 3810,and may be refracted or diffracted by grating coupler 3820.

The angular-selective transmissive layer 3840 described above may beimplemented in various ways. In some embodiments, the angular-selectivetransmissive layer may include one or more dielectric layers (or airgap). Each dielectric layer may have a respective refractive index, andadjacent dielectric layers may have different refractive indexes. Insome embodiments, the angular-selective transmissive layer may include,for example, micro mirrors or prisms, grating, meta-gratings, nanowires,nano-pillars, or other micro- or nano-structures. In some examples, theangular-selective transmissive layer may include gratings (e.g.,surface-relief gratings or holographic gratings) with small gratingperiods formed on a substrate. The gratings may only diffract light withlarge incidence angles (e.g., about 75° to about 90°) and the diffractedlight may propagate in directions such that the diffracted light may notreach the eyebox. The grating period may be, for example, less than 280nm (e.g., about 200 nm) such that the angular-selective transmissivelayer may not affect light within the see-through field of view. In someexamples, the angular-selective transmissive layer may includemicro-scale or nano-scale anisotropic structures that may reflect,diffract, or absorb incident light with large incident angles. Theanisotropic structures may include, for example, large-aspect-rationanoparticles aligned and immersed in transparent media, nanowirearrays, certain liquid crystal materials, and the like.

Embodiments of the invention may be used to implement components of anartificial reality system or may be implemented in conjunction with anartificial reality system. Artificial reality is a form of reality thathas been adjusted in some manner before presentation to a user, whichmay include, for example, a virtual reality (VR), an augmented reality(AR), a mixed reality (MR), a hybrid reality, or some combination and/orderivatives thereof. Artificial reality content may include completelygenerated content or generated content combined with captured (e.g.,real-world) content. The artificial reality content may include video,audio, haptic feedback, or some combination thereof, and any of whichmay be presented in a single channel or in multiple channels (such asstereo video that produces a three-dimensional effect to the viewer).Additionally, in some embodiments, artificial reality may also beassociated with applications, products, accessories, services, or somecombination thereof, that are used to, for example, create content in anartificial reality and/or are otherwise used in (e.g., performactivities in) an artificial reality. The artificial reality system thatprovides the artificial reality content may be implemented on variousplatforms, including a head-mounted display (HMD) connected to a hostcomputer system, a standalone HMD, a mobile device or computing system,or any other hardware platform capable of providing artificial realitycontent to one or more viewers.

FIG. 39 is a simplified block diagram of an example electronic system3900 of an example near-eye display (e.g., HMD device) for implementingsome of the examples disclosed herein. Electronic system 3900 may beused as the electronic system of an HMD device or other near-eyedisplays described above. In this example, electronic system 3900 mayinclude one or more processor(s) 3910 and a memory 3920. Processor(s)3910 may be configured to execute instructions for performing operationsat a number of components, and can be, for example, a general-purposeprocessor or microprocessor suitable for implementation within aportable electronic device. Processor(s) 3910 may be communicativelycoupled with a plurality of components within electronic system 3900. Torealize this communicative coupling, processor(s) 3910 may communicatewith the other illustrated components across a bus 3940. Bus 3940 may beany subsystem adapted to transfer data within electronic system 3900.Bus 3940 may include a plurality of computer buses and additionalcircuitry to transfer data.

Memory 3920 may be coupled to processor(s) 3910. In some embodiments,memory 3920 may offer both short-term and long-term storage and may bedivided into several units. Memory 3920 may be volatile, such as staticrandom access memory (SRAM) and/or dynamic random access memory (DRAM)and/or non-volatile, such as read-only memory (ROM), flash memory, andthe like. Furthermore, memory 3920 may include removable storagedevices, such as secure digital (SD) cards. Memory 3920 may providestorage of computer-readable instructions, data structures, programmodules, and other data for electronic system 3900. In some embodiments,memory 3920 may be distributed into different hardware modules. A set ofinstructions and/or code might be stored on memory 3920. Theinstructions might take the form of executable code that may beexecutable by electronic system 3900, and/or might take the form ofsource and/or installable code, which, upon compilation and/orinstallation on electronic system 3900 (e.g., using any of a variety ofgenerally available compilers, installation programs,compression/decompression utilities, etc.), may take the form ofexecutable code.

In some embodiments, memory 3920 may store a plurality of applicationmodules 3922 through 3924, which may include any number of applications.Examples of applications may include gaming applications, conferencingapplications, video playback applications, or other suitableapplications. The applications may include a depth sensing function oreye tracking function. Application modules 3922-3924 may includeparticular instructions to be executed by processor(s) 3910. In someembodiments, certain applications or parts of application modules3922-3924 may be executable by other hardware modules 3980. In certainembodiments, memory 3920 may additionally include secure memory, whichmay include additional security controls to prevent copying or otherunauthorized access to secure information.

In some embodiments, memory 3920 may include an operating system 3925loaded therein. Operating system 3925 may be operable to initiate theexecution of the instructions provided by application modules 3922-3924and/or manage other hardware modules 3980 as well as interfaces with awireless communication subsystem 3930 which may include one or morewireless transceivers. Operating system 3925 may be adapted to performother operations across the components of electronic system 3900including threading, resource management, data storage control and othersimilar functionality.

Wireless communication subsystem 3930 may include, for example, aninfrared communication device, a wireless communication device and/orchipset (such as a Bluetooth® device, an IEEE 802.11 device, a Wi-Fidevice, a WiMax device, cellular communication facilities, etc.), and/orsimilar communication interfaces. Electronic system 3900 may include oneor more antennas 3934 for wireless communication as part of wirelesscommunication subsystem 3930 or as a separate component coupled to anyportion of the system. Depending on desired functionality, wirelesscommunication subsystem 3930 may include separate transceivers tocommunicate with base transceiver stations and other wireless devicesand access points, which may include communicating with different datanetworks and/or network types, such as wireless wide-area networks(WWANs), wireless local area networks (WLANs), or wireless personal areanetworks (WPANs). A WWAN may be, for example, a WiMax (IEEE 802.16)network. A WLAN may be, for example, an IEEE 802.11x network. A WPAN maybe, for example, a Bluetooth network, an IEEE 802.15x, or some othertypes of network. The techniques described herein may also be used forany combination of WWAN, WLAN, and/or WPAN. Wireless communicationssubsystem 3930 may permit data to be exchanged with a network, othercomputer systems, and/or any other devices described herein. Wirelesscommunication subsystem 3930 may include a means for transmitting orreceiving data, such as identifiers of HMD devices, position data, ageographic map, a heat map, photos, or videos, using antenna(s) 3934 andwireless link(s) 3932. Wireless communication subsystem 3930,processor(s) 3910, and memory 3920 may together comprise at least a partof one or more of a means for performing some functions disclosedherein.

Embodiments of electronic system 3900 may also include one or moresensors 3990. Sensor(s) 3990 may include, for example, an image sensor,an accelerometer, a pressure sensor, a temperature sensor, a proximitysensor, a magnetometer, a gyroscope, an inertial sensor (e.g., a modulethat combines an accelerometer and a gyroscope), an ambient lightsensor, or any other similar module operable to provide sensory outputand/or receive sensory input, such as a depth sensor or a positionsensor. For example, in some implementations, sensor(s) 3990 may includeone or more inertial measurement units (IMUs) and/or one or moreposition sensors. An IMU may generate calibration data indicating anestimated position of the HMD device relative to an initial position ofthe HMD device, based on measurement signals received from one or moreof the position sensors. A position sensor may generate one or moremeasurement signals in response to motion of the HMD device. Examples ofthe position sensors may include, but are not limited to, one or moreaccelerometers, one or more gyroscopes, one or more magnetometers,another suitable type of sensor that detects motion, a type of sensorused for error correction of the IMU, or some combination thereof. Theposition sensors may be located external to the IMU, internal to theIMU, or some combination thereof. At least some sensors may use astructured light pattern for sensing.

Electronic system 3900 may include a display module 3960. Display module3960 may be a near-eye display, and may graphically present information,such as images, videos, and various instructions, from electronic system3900 to a user. Such information may be derived from one or moreapplication modules 3922-3924, virtual reality engine 3926, one or moreother hardware modules 3980, a combination thereof, or any othersuitable means for resolving graphical content for the user (e.g., byoperating system 3925). Display module 3960 may use liquid crystaldisplay (LCD) technology, light-emitting diode (LED) technology(including, for example, OLED, ILED, μLED, AMOLED, TOLED, etc.), lightemitting polymer display (LPD) technology, or some other displaytechnology.

Electronic system 3900 may include a user input/output module 3970. Userinput/output module 3970 may allow a user to send action requests toelectronic system 3900. An action request may be a request to perform aparticular action. For example, an action request may be to start or endan application or to perform a particular action within the application.User input/output module 3970 may include one or more input devices.Example input devices may include a touchscreen, a touch pad,microphone(s), button(s), dial(s), switch(es), a keyboard, a mouse, agame controller, or any other suitable device for receiving actionrequests and communicating the received action requests to electronicsystem 3900. In some embodiments, user input/output module 3970 mayprovide haptic feedback to the user in accordance with instructionsreceived from electronic system 3900. For example, the haptic feedbackmay be provided when an action request is received or has beenperformed.

Electronic system 3900 may include a camera 3950 that may be used totake photos or videos of a user, for example, for tracking the user'seye position. Camera 3950 may also be used to take photos or videos ofthe environment, for example, for VR, AR, or MR applications. Camera3950 may include, for example, a complementary metal-oxide-semiconductor(CMOS) image sensor with a few millions or tens of millions of pixels.In some implementations, camera 3950 may include two or more camerasthat may be used to capture 3-D images.

In some embodiments, electronic system 3900 may include a plurality ofother hardware modules 3980. Each of other hardware modules 3980 may bea physical module within electronic system 3900. While each of otherhardware modules 3980 may be permanently configured as a structure, someof other hardware modules 3980 may be temporarily configured to performspecific functions or temporarily activated. Examples of other hardwaremodules 3980 may include, for example, an audio output and/or inputmodule (e.g., a microphone or speaker), a near field communication (NFC)module, a rechargeable battery, a battery management system, awired/wireless battery charging system, etc. In some embodiments, one ormore functions of other hardware modules 3980 may be implemented insoftware.

In some embodiments, memory 3920 of electronic system 3900 may alsostore a virtual reality engine 3926. Virtual reality engine 3926 mayexecute applications within electronic system 3900 and receive positioninformation, acceleration information, velocity information, predictedfuture positions, or some combination thereof of the HMD device from thevarious sensors. In some embodiments, the information received byvirtual reality engine 3926 may be used for producing a signal (e.g.,display instructions) to display module 3960. For example, if thereceived information indicates that the user has looked to the left,virtual reality engine 3926 may generate content for the HMD device thatmirrors the user's movement in a virtual environment. Additionally,virtual reality engine 3926 may perform an action within an applicationin response to an action request received from user input/output module3970 and provide feedback to the user. The provided feedback may bevisual, audible, or haptic feedback. In some implementations,processor(s) 3910 may include one or more GPUs that may execute virtualreality engine 3926.

In various implementations, the above-described hardware and modules maybe implemented on a single device or on multiple devices that cancommunicate with one another using wired or wireless connections. Forexample, in some implementations, some components or modules, such asGPUs, virtual reality engine 3926, and applications (e.g., trackingapplication), may be implemented on a console separate from thehead-mounted display device. In some implementations, one console may beconnected to or support more than one HMD.

In alternative configurations, different and/or additional componentsmay be included in electronic system 3900. Similarly, functionality ofone or more of the components can be distributed among the components ina manner different from the manner described above. For example, in someembodiments, electronic system 3900 may be modified to include othersystem environments, such as an AR system environment and/or an MRenvironment.

The methods, systems, and devices discussed above are examples. Variousembodiments may omit, substitute, or add various procedures orcomponents as appropriate. For instance, in alternative configurations,the methods described may be performed in an order different from thatdescribed, and/or various stages may be added, omitted, and/or combined.Also, features described with respect to certain embodiments may becombined in various other embodiments. Different aspects and elements ofthe embodiments may be combined in a similar manner. Also, technologyevolves and, thus, many of the elements are examples that do not limitthe scope of the disclosure to those specific examples.

Specific details are given in the description to provide a thoroughunderstanding of the embodiments. However, embodiments may be practicedwithout these specific details. For example, well-known circuits,processes, systems, structures, and techniques have been shown withoutunnecessary detail in order to avoid obscuring the embodiments. Thisdescription provides example embodiments only, and is not intended tolimit the scope, applicability, or configuration of the invention.Rather, the preceding description of the embodiments will provide thoseskilled in the art with an enabling description for implementing variousembodiments. Various changes may be made in the function and arrangementof elements without departing from the spirit and scope of the presentdisclosure.

Also, some embodiments were described as processes depicted as flowdiagrams or block diagrams. Although each may describe the operations asa sequential process, many of the operations may be performed inparallel or concurrently. In addition, the order of the operations maybe rearranged. A process may have additional steps not included in thefigure. Furthermore, embodiments of the methods may be implemented byhardware, software, firmware, middleware, microcode, hardwaredescription languages, or any combination thereof. When implemented insoftware, firmware, middleware, or microcode, the program code or codesegments to perform the associated tasks may be stored in acomputer-readable medium such as a storage medium. Processors mayperform the associated tasks.

It will be apparent to those skilled in the art that substantialvariations may be made in accordance with specific requirements. Forexample, customized or special-purpose hardware might also be used,and/or particular elements might be implemented in hardware, software(including portable software, such as applets, etc.), or both. Further,connection to other computing devices such as network input/outputdevices may be employed.

With reference to the appended figures, components that can includememory can include non-transitory machine-readable media. The term“machine-readable medium” and “computer-readable medium” may refer toany storage medium that participates in providing data that causes amachine to operate in a specific fashion. In embodiments providedhereinabove, various machine-readable media might be involved inproviding instructions/code to processing units and/or other device(s)for execution. Additionally or alternatively, the machine-readable mediamight be used to store and/or carry such instructions/code. In manyimplementations, a computer-readable medium is a physical and/ortangible storage medium. Such a medium may take many forms, including,but not limited to, non-volatile media, volatile media, and transmissionmedia. Common forms of computer-readable media include, for example,magnetic and/or optical media such as compact disk (CD) or digitalversatile disk (DVD), punch cards, paper tape, any other physical mediumwith patterns of holes, a RAM, a programmable read-only memory (PROM),an erasable programmable read-only memory (EPROM), a FLASH-EPROM, anyother memory chip or cartridge, a carrier wave as described hereinafter,or any other medium from which a computer can read instructions and/orcode. A computer program product may include code and/ormachine-executable instructions that may represent a procedure, afunction, a subprogram, a program, a routine, an application (App), asubroutine, a module, a software package, a class, or any combination ofinstructions, data structures, or program statements.

Those of skill in the art will appreciate that information and signalsused to communicate the messages described herein may be representedusing any of a variety of different technologies and techniques. Forexample, data, instructions, commands, information, signals, bits,symbols, and chips that may be referenced throughout the abovedescription may be represented by voltages, currents, electromagneticwaves, magnetic fields or particles, optical fields or particles, or anycombination thereof.

Terms, “and” and “or” as used herein, may include a variety of meaningsthat are also expected to depend at least in part upon the context inwhich such terms are used. Typically, “or” if used to associate a list,such as A, B, or C, is intended to mean A, B, and C, here used in theinclusive sense, as well as A, B, or C, here used in the exclusivesense. In addition, the term “one or more” as used herein may be used todescribe any feature, structure, or characteristic in the singular ormay be used to describe some combination of features, structures, orcharacteristics. However, it should be noted that this is merely anillustrative example and claimed subject matter is not limited to thisexample. Furthermore, the term “at least one of” if used to associate alist, such as A, B, or C, can be interpreted to mean any combination ofA, B, and/or C, such as A, AB, AC, BC, AA, ABC, AAB, AABBCCC, etc.

Further, while certain embodiments have been described using aparticular combination of hardware and software, it should be recognizedthat other combinations of hardware and software are also possible.Certain embodiments may be implemented only in hardware, or only insoftware, or using combinations thereof. In one example, software may beimplemented with a computer program product containing computer programcode or instructions executable by one or more processors for performingany or all of the steps, operations, or processes described in thisdisclosure, where the computer program may be stored on a non-transitorycomputer readable medium. The various processes described herein can beimplemented on the same processor or different processors in anycombination.

Where devices, systems, components or modules are described as beingconfigured to perform certain operations or functions, suchconfiguration can be accomplished, for example, by designing electroniccircuits to perform the operation, by programming programmableelectronic circuits (such as microprocessors) to perform the operationsuch as by executing computer instructions or code, or processors orcores programmed to execute code or instructions stored on anon-transitory memory medium, or any combination thereof. Processes cancommunicate using a variety of techniques, including, but not limitedto, conventional techniques for inter-process communications, anddifferent pairs of processes may use different techniques, or the samepair of processes may use different techniques at different times.

The specification and drawings are, accordingly, to be regarded in anillustrative rather than a restrictive sense. It will, however, beevident that additions, subtractions, deletions, and other modificationsand changes may be made thereunto without departing from the broaderspirit and scope as set forth in the claims. Thus, although specificembodiments have been described, these are not intended to be limiting.Various modifications and equivalents are within the scope of thefollowing claims.

What is claimed is:
 1. A waveguide display comprising: a substrate; afirst reflection volume Bragg grating (VBG) on the substrate andcharacterized by a first refractive index modulation; and a secondreflection VBG on the substrate and including a first region and asecond region, wherein the first reflection VBG is configured todiffract display light in a first wavelength range such that the displaylight in the first wavelength range propagates in the substrate throughtotal internal reflection to the first region and the second region ofthe second reflection VBG; wherein the first region of the secondreflection VBG is characterized by a second refractive index modulationlower than the first refractive index modulation and is configured todiffract display light in a second wavelength range that is within thefirst wavelength range; and wherein the second region of the secondreflection VBG is characterized by a third refractive index modulationgreater than the second refractive index modulation and is configured todiffract display light in a third wavelength range that includes and islarger than the second wavelength range.
 2. The waveguide display ofclaim 1, wherein the first region and the second region of the secondreflection VBG are arranged such that the display light in the firstwavelength range reaches the first region before reaching the secondregion.
 3. The waveguide display of claim 1, wherein: the thirdrefractive index modulation is equal to or less than the firstrefractive index modulation; and the first wavelength range is the sameas or includes the third wavelength range.
 4. The waveguide display ofclaim 1, wherein the first reflection VBG and the second reflection VBGhave a same grating vector in a plane perpendicular to a surface normaldirection of the substrate.
 5. The waveguide display of claim 1, whereinthe second reflection VBG further includes a third region between thefirst region and the second region, the third region characterized by afourth refractive index modulation greater than the second refractiveindex modulation but lower than the third refractive index modulationand configured to diffract display light in a fourth wavelength rangethat includes the second wavelength range and is within the thirdwavelength range.
 6. The waveguide display of claim 1, furthercomprising: a third reflection VBG multiplexed with the first reflectionVBG and characterized by a fourth refractive index modulation; and afourth reflection VBG multiplexed with the second reflection VBG in thefirst region and second region, wherein the third reflection VBG isconfigured to diffract display light in a fourth wavelength range suchthat the display light in the fourth wavelength range propagates in thesubstrate through total internal reflection to the first region and thesecond region of the fourth reflection VBG; wherein the first region ofthe fourth reflection VBG is characterized by a fifth refractive indexmodulation lower than the fourth refractive index modulation and isconfigured to diffract display light in a fifth wavelength range that iswithin the fourth wavelength range; and wherein the second region of thefourth reflection VBG is characterized by a sixth refractive indexmodulation greater than the fifth refractive index modulation and isconfigured to diffract display light in a sixth wavelength range thatincludes and is larger than the fifth wavelength range.
 7. The waveguidedisplay of claim 1, wherein the first reflection VBG is configured to:diffract display light in the first wavelength range and a first fieldof view (FOV) range; and diffract display light in a fourth wavelengthrange and a second FOV range different from the first FOV range.
 8. Thewaveguide display of claim 1, wherein: the substrate is transparent tovisible light; and the second reflection VBG is transparent to visiblelight from an ambient environment.
 9. The waveguide display of claim 1,wherein: the first reflection VBG is configured to couple the displaylight in the first wavelength range into the substrate; and the secondreflection VBG is configured to couple the display light in the firstwavelength range out of the substrate.
 10. The waveguide display ofclaim 9, further comprising a third grating and a fourth grating,wherein: the third grating is configured to diffract the display lightin the first wavelength range from the first reflection VBG to thefourth grating; and the fourth grating is configured to diffract thedisplay light in the first wavelength range at two or more regions ofthe fourth grating to the second reflection VBG.
 11. The waveguidedisplay of claim 10, wherein the third grating and the fourth gratinghave a same grating vector in a plane perpendicular to a surface normaldirection of the substrate.
 12. The waveguide display of claim 1,further comprising: an input coupler configured to couple the displaylight in the first wavelength range into the substrate; and an outputcoupler configured to couple the display light diffracted by the secondreflection VBG out of the substrate.
 13. The waveguide display of claim12, wherein the input coupler and the output coupler include multiplexedVBGs.
 14. The waveguide display of claim 1, further comprising: a lightsource configured to generate the display light; and projector opticsconfigured to collimate the display light and direct the display lightto the first reflection VBG.